AC Circuits questions

The opposite figure shows the structure of an electrical measuring instrument, then:
(1) The working idea of this instrument depends on ..........

1. A eddy currents
2. B the magnetic effect of electric current
3. C the heating effect of electric current
4. D electromagnetic induction

The opposite figure shows the structure of an electrical measuring instrument, then:
(2) The resistance R is used for ..........

1. A heating the wire faster
2. B keeping the silk thread always taut
3. C increasing the current range of the instrument
4. D increasing the resistance of the instrument

The opposite figure shows the structure of an electrical measuring instrument, then:
(3) The part made of platinum-iridium is ..........

1. A component (1)
2. B component (2)
3. C component (3)
4. D component (4)

The opposite figure shows the structure of an electrical measuring instrument, then:
(4) The function of component (3) is ..........

1. A making the scale of the instrument uniform
2. B increasing the range of the instrument
3. C keeping the silk thread always taut
4. D heating the instrument when the current passes

The opposite figure shows the structure of an electrical measuring instrument, then:
(5) The electric current passes through ..........

1. A component (1) and component (3)
2. B component (2) and component (5)
3. C component (1) and the resistance R
4. D component (2) and the resistance R

In a hot-wire ammeter, the heat power produced in the platinum-iridium wire by an alternating current passing through it is directly proportional to ..........

1. A the effective value of the current
2. B the reciprocal of the effective value of the current
3. C the maximum value of the current
4. D the square of the effective value of the current

An alternating current of maximum value 14 A passing through the wire of a hot-wire ammeter produces a certain heat power. To produce the same heat power in the wire, a direct current must pass through it of about ..........

1. A 7 A
2. B 10 A
3. C 14 A
4. D 20 A

The platinum-iridium wire of a hot-wire ammeter is connected in parallel with a shunt, and the ammeter is connected to a circuit carrying an alternating current of effective value I. If the shunt resistance is increased and the same current (I) passes in the circuit, the heat power produced in the wire ..........

1. A increases
2. B decreases
3. C does not change
4. D cannot be determined

In the opposite figure, a hot-wire ammeter carries an electric current (I). When the shunt $(R_s)$ is decreased and the same current (I) passes through the ammeter, what happens to:
(1) the range and the accuracy of the ammeter, respectively?

1. A decreases, decreases
2. B decreases, increases
3. C increases, decreases
4. D increases, increases

In the opposite figure, a hot-wire ammeter carries an electric current (I). When the shunt $(R_s)$ is decreased and the same current (I) passes through the ammeter, what happens to:
(2) the tension in the spring?

1. A increases
2. B decreases
3. C does not change
4. D cannot be determined

Which of the following figures correctly shows the scale of a hot-wire ammeter?

1. A A
2. B B
3. C C
4. D D

If the pointer of a hot-wire ammeter deflects as shown in the opposite figure when an alternating current of effective value I passes, which of the following figures correctly shows the position of the pointer when an alternating current of effective value 2 I passes through the ammeter?

1. A A
2. B B
3. C C
4. D D

In the electric circuit shown, a hot-wire ammeter of resistance R is connected to an AC source of effective voltage V. When only switch $K_1$ is closed, the pointer deflects by an angle θ from zero, and when only switch $K_2$ is closed, the pointer deflects by an angle 9θ from zero. The resistance $R_x$ equals ..........

1. A 4 R
2. B 2 R
3. C R
4. D 0.5 R

A student divided the distance between the zero position (O) and the position of the maximum possible reading (D) on the scale of a hot-wire ammeter into four equal parts, as in the opposite figure. The part that shows the largest change in current is ..........

1. A OA
2. B AB
3. C BC
4. D CD

The opposite figure shows the scale of a hot-wire ammeter. The values of the two angles $(\theta_1)$ and $(\theta_2)$ shown in the figure are, respectively, ..........

1. A 20°, 40°
2. B 40°, 50°
3. C 30°, 50°
4. D 30°, 40°

The opposite graph shows the alternating current in a circuit containing a hot-wire ammeter. The reading of the hot-wire ammeter equals the instantaneous value of the current after a time from the start of the cycle equal to ..........

1. A 0.5 ms
2. B 1 ms
3. C 2 ms
4. D 4 ms

In the electric circuit shown, when switch K is closed a current of 1 A passes and the pointer of each ammeter deflects by the same angle. When a current of 2 A passes, the pointer of ammeter x deflects by an angle θ, so the pointer of ammeter y deflects by an angle ..........

1. A smaller than θ
2. B greater than θ
3. C equal to θ
4. D cannot be determined

The opposite graph shows the relation between the deflection angle of the pointer of a hot-wire ammeter (θ) and the quantity (x). Which of the curves (a), (b), (c), (d) shown represents this relation correctly, if the quantity (x) is:
(1) the electric power consumed in the platinum-iridium wire?

1. A curve (a)
2. B curve (b)
3. C curve (c)
4. D curve (d)

The opposite graph shows the relation between the deflection angle of the pointer of a hot-wire ammeter (θ) and the quantity (x). Which of the curves (a), (b), (c), (d) shown represents this relation correctly, if the quantity (x) is:
(2) the electric current passing through the platinum-iridium wire?

1. A curve (a)
2. B curve (b)
3. C curve (c)
4. D curve (d)

The opposite circuit is used to calibrate a hot-wire ammeter. It was noticed that the pointer of the moving-coil ammeter points exactly to zero while the pointer of the hot-wire ammeter shows a reading greater than zero. This means that the expansion coefficient of the plate on which the platinum-iridium wire is fixed is .......... the expansion coefficient of the wire.

1. A greater than
2. B less than
3. C equal to
4. D cannot be determined

A hot-wire ammeter and a moving-coil ammeter are connected in a circuit as in the opposite figure. When switch (K) is closed, which ammeter's pointer settles first at a definite reading?

1. A the hot-wire ammeter
2. B the moving-coil ammeter
3. C both pointers settle together
4. D neither pointer moves from zero

Each of the following figures shows the scale of one of three electrical measuring instruments (1), (2), (3). Which of these instruments is used:
(1) to measure direct current only?

1. A instrument 1
2. B instrument 2
3. C instrument 3
4. D instruments 1 and 3

Each of the following figures shows the scale of one of three electrical measuring instruments (1), (2), (3). Which of these instruments is used:
(2) to measure the effective value of an alternating current?

1. A instrument 1
2. B instrument 2
3. C instrument 3
4. D instruments 1 and 3

Each of the following figures shows the scale of one of three electrical measuring instruments (1), (2), (3). Which of these instruments is used:
(3) to measure an unknown ohmic resistance?

1. A instrument 1
2. B instrument 2
3. C instrument 3
4. D instruments 1 and 3

Each of the following figures shows the scale of one of three electrical measuring instruments (1), (2), (3). Which of these instruments is used:
(4) to find the direction of the current in the circuit?

1. A instrument 1
2. B instrument 2
3. C instrument 3
4. D instruments 1 and 3

In the opposite circuit, the alternating voltage across the resistance (R) is ..........

1. A in phase with the current
2. B leading the current by a phase angle of 90°
3. C lagging behind the current by $\dfrac{3}{4}$ of a cycle
4. D numerically equal to the current

An AC source is connected to an ohmic resistance of 100 Ω. If the instantaneous emf of the source is given by $V = 424.27 \sin \omega t$, the power consumed in the ohmic resistance equals ..........

1. A 760 W
2. B 820 W
3. C 850 W
4. D 900 W

In the opposite circuit, the voltage across the resistance $R_1$ .......... the voltage across the resistance $R_2$

1. A leads by a phase angle of 40°
2. B leads by a phase angle of 50°
3. C lags by a phase angle of 50° behind
4. D is in phase with

Which of the following graphs shows the relation between the maximum value of the alternating current $(I_{max})$ in an ohmic resistance connected to a dynamo of negligible internal resistance and the frequency of rotation of the dynamo coil (f)?

1. A A
2. B B
3. C C
4. D D

Two identical lamps (x) and (y): lamp (x) is connected to a dynamo of maximum voltage 60 V and frequency 50 Hz as shown in circuit (1), and lamp (y) is connected to a DC source of emf 60 V, negligible internal resistance and adjustable voltage, as shown in circuit (2). To make the two lamps equally bright, we can ..........

1. A increase $(V_B)$ to $60\sqrt{2}$ V
2. B decrease $(V_B)$ to 30 V
3. C increase the dynamo frequency to $50\sqrt{2}$ Hz
4. D decrease the dynamo frequency to $\dfrac{50}{\sqrt{2}}$ Hz

Three resistances R, 2 R and 6 R are connected to an AC source as shown in the opposite circuit. If the instantaneous potential difference across the source is given by $V = 300\sqrt{2} \sin (100 \pi t)$, and the effective current in branch (cd) equals 1 A, then:
(1) The instantaneous value of the total current in the circuit is given by ..........

1. A $I = 3 \sin (100 \pi t)$
2. B $I = 3\sqrt{2} \sin (100 \pi t)$
3. C $I = 3 \sin \left(100 \pi t + \dfrac{\pi}{2}\right)$
4. D $I = 3\sqrt{2} \sin \left(100 \pi t + \dfrac{\pi}{2}\right)$

Three resistances R, 2 R and 6 R are connected to an AC source as shown in the opposite circuit. If the instantaneous potential difference across the source is given by $V = 300\sqrt{2} \sin (100 \pi t)$, and the effective current in branch (cd) equals 1 A, then:
(2) The resistance (R) equals ..........

1. A 25 Ω
2. B 50 Ω
3. C 100 Ω
4. D 200 Ω

If the potential difference (V) across an inductor of no ohmic resistance connected to an AC source changes with time (t) as in the opposite graph, the graph that shows how the current (I) in the coil changes with time (t) during the same period is ..........

1. A A
2. B B
3. C C
4. D D

If the inductive reactance of a coil connected to an AC source is (440 L) Ω, where (L) is the self-inductance of the coil, the frequency of the current is ..........

1. A 140 Hz
2. B 400 Hz
3. C 70 Hz
4. D 44 Hz

An inductor has an inductive reactance of 1000 Ω. If both the self-inductance of the coil and the frequency of the current in it are doubled, its inductive reactance becomes ..........

1. A 2000 Ω
2. B 500 Ω
3. C 250 Ω
4. D 4000 Ω

An alternating current of effective value 100 mA passes through an inductor of no ohmic resistance and self-inductance 0.1 H. If the frequency of the current is 50 Hz, the effective potential difference across the coil equals ..........

1. A 3.14 V
2. B 31.4 V
3. C 314 V
4. D 3140 V

An AC dynamo of negligible internal resistance has its terminals connected to an inductor of negligible ohmic resistance. Which of the following graphs shows the relation between:
(1) the inductive reactance $(X_L)$ of the coil and the frequency (f) of rotation of the dynamo coil?

1. A A
2. B B
3. C C
4. D D

An AC dynamo of negligible internal resistance has its terminals connected to an inductor of negligible ohmic resistance. Which of the following graphs shows the relation between:
(2) the current (I) in the coil and the frequency (f) of rotation of the dynamo coil?

1. A A
2. B B
3. C C
4. D D

An AC dynamo of negligible internal resistance has its terminals connected to an inductor of negligible ohmic resistance. Which of the following graphs shows the relation between:
(3) the electric power $(P_w)$ consumed in the coil and the frequency (f) of rotation of the dynamo coil?

1. A A
2. B B
3. C C
4. D D

An inductor of no resistance and adjustable self-inductance is connected to an AC source of frequency f. The opposite graph shows the relation between the inductive reactance of the coil $(X_L)$ and its self-inductance (L). The frequency of the current (f) equals ..........

1. A 150.1 Hz
2. B 159.1 Hz
3. C 162.1 Hz
4. D 165.1 Hz

The opposite figure shows the graph of the inductive reactance of a coil against the frequency of the current in it. The self-inductance of the coil is ..........

1. A 0.01 H
2. B 0.02 H
3. C $\dfrac{1}{100\pi}$ H
4. D $\dfrac{1}{50\pi}$ H

The opposite graph shows the relation between the inductive reactance $(X_L)$ of two inductors of self-inductances $L_1$ and $L_2$ and the frequency (f) of the alternating current in each. The relation between them is ..........

1. A $L_1 = L_2 \neq 0$
2. B $L_1 > L_2$
3. C $L_1 < L_2$
4. D $L_1 = L_2 = 0$

Two solenoids A and B are connected together in series to an AC dynamo whose coil speed can be changed. The opposite figure shows the graph of the inductive reactance $(X_L)$ of each coil against the angular velocity (ω) of the dynamo coil. The ratio between the self-inductances of the two coils $\left(\frac{L_A}{L_B}\right)$ equals ..........

1. A 0.02
2. B 0.15
3. C $\dfrac{\sqrt{3}}{2}$
4. D $\dfrac{\sqrt{3}}{3}$

An inductor of no ohmic resistance is connected to an AC source, and the instantaneous potential difference across the coil is given by $V = 66 \sin (116 \pi t)$. If the maximum current in the circuit is 2 A, the self-inductance of the coil is about ..........

1. A 0.02 H
2. B 0.05 H
3. C 0.06 H
4. D 0.09 H

An inductor is connected to an AC source. The instantaneous values of the potential difference across the coil and of the current in it are given by the two equations:
(1) $V = 200 \sin (50 \pi t)$
(2) $I = 2 \sin \left(50 \pi t - \frac{\pi}{2}\right)$
The self-inductance of the coil and the frequency of the source are ..........

1. A self-inductance: $\dfrac{2}{\pi}$ H, source frequency: 25 Hz
2. B self-inductance: $\dfrac{2}{\pi}$ H, source frequency: 50 Hz
3. C self-inductance: π H, source frequency: 25 Hz
4. D self-inductance: π H, source frequency: 50 Hz

A circuit consists of an inductor of no ohmic resistance and an AC source of constant frequency whose emf can be changed. The graph that shows the relation between the effective current $(I_{eff})$ and the effective potential difference $(V_L)_{eff}$ across the coil is ..........

1. A A
2. B B
3. C C
4. D D

Several solenoids with different numbers of turns, each of area $(A_0)$, length 79 cm and core permeability $2 \times 10^{-3}$ T.m/A, carry an alternating current of frequency 50 Hz. The opposite graph shows the relation between the inductive reactance $(X_L)$ of each coil and the square of its number of turns $(N^2)$. The area of any of the coils $(A_0)$ equals ..........

1. A 6.28 cm²
2. B 12.6 cm²
3. C 25.1 cm²
4. D 62.8 cm²

The opposite figure shows two solenoids a and b with the same length and the same number of turns. The cross-sectional area of coil b is twice that of coil a. The ratio of their inductive reactances $\left(\frac{(X_L)_a}{(X_L)_b}\right)$ when connected to the same AC source equals ..........

1. A $\dfrac{1}{2}$
2. B $\dfrac{3}{1}$
3. C $\dfrac{1}{1}$
4. D $\dfrac{2}{1}$

In the opposite figure, an inductor of self-inductance L is connected to an AC source of frequency f, and the inductive reactance of the coil is $X_L$. If the coil is cut into three identical parts and one part is connected to the same source, the self-inductance and the inductive reactance of the coil become, respectively, ..........

1. A $\dfrac{L}{3}$, $\dfrac{X_L}{3}$
2. B 3 L, $\dfrac{X_L}{3}$
3. C $\dfrac{L}{3}$, 3 $X_L$
4. D 3 L, 3 $X_L$

An air-core inductor of self-inductance L is connected to an AC source of frequency f, and its inductive reactance is $X_L$. If a soft iron rod is inserted into the coil, then ..........

1. A self-inductance: increases, inductive reactance: decreases
2. B self-inductance: decreases, inductive reactance: increases
3. C self-inductance: increases, inductive reactance: increases
4. D self-inductance: decreases, inductive reactance: decreases

A coil of self-inductance 0.7 H and negligible resistance is connected to an AC source of emf 120 V and frequency 50 Hz, then:
(1) The inductive reactance of the coil is ..........

1. A 110 Ω
2. B 200 Ω
3. C 220 Ω
4. D 300 Ω

A coil of self-inductance 0.7 H and negligible resistance is connected to an AC source of emf 120 V and frequency 50 Hz, then:
(2) The effective current in the circuit is ..........

1. A 0.4 A
2. B 0.55 A
3. C 0.6 A
4. D 1.09 A

In the circuit shown, if the reading of the hot-wire ammeter is 4 A, the self-inductance of the coil equals .......... (given that the ohmic resistance of the coil and the ammeter is negligible)

1. A 0.191 H
2. B 0.21 H
3. C 0.251 H
4. D 0.3 H

An AC source of maximum voltage 100 V has its terminals connected to an inductor of negligible ohmic resistance with 132 turns, each of area $10^{-3}$ m², and a core permeability of $2 \times 10^{-3}$ T.m/A. The maximum current in it is 4 A and it lags behind the maximum voltage by 6.25 ms. The length of the coil equals ..........

1. A 17.5 cm
2. B 35 cm
3. C 70 cm
4. D 100 cm

An inductor of negligible ohmic resistance has an inductive reactance of 15 Ω when an alternating current of frequency $f_1$ passes through it. If the frequency increases by 20 Hz to become $f_2$, its inductive reactance becomes 25 Ω. The frequency of the current in the second case $(f_2)$ equals ..........

1. A 30 Hz
2. B 40 Hz
3. C 50 Hz
4. D 60 Hz

An inductor of negligible ohmic resistance has an inductive reactance of 12 Ω when an alternating current of frequency f passes through it. If the frequency of the current increases by 20 Hz, its inductive reactance becomes 18 Ω, then:
(1) The ratio of the frequency of the current in the first case to that in the second case is ..........

1. A $\dfrac{3}{2}$
2. B $\dfrac{2}{3}$
3. C $\dfrac{2}{1}$
4. D $\dfrac{1}{2}$

An inductor of negligible ohmic resistance has an inductive reactance of 12 Ω when an alternating current of frequency f passes through it. If the frequency of the current increases by 20 Hz, its inductive reactance becomes 18 Ω, then:
(2) The self-inductance of the coil is ..........

1. A 0.021 H
2. B 0.031 H
3. C 0.048 H
4. D 0.071 H

A single-layer coil of 300 turns, radius 2.1 cm and length 15 cm is wound around a cylindrical iron rod of permeability 0.002 Wb/A.m and connected to a source of frequency 50 Hz. The inductive reactance of the coil equals ..........

1. A 225.3 Ω
2. B 341.4 Ω
3. C 425.3 Ω
4. D 522.7 Ω

Two AC sources (1) and (2) have the same effective voltage. Source (1) is connected to an inductor (x) of negligible ohmic resistance, and source (2) to an inductor (y) of negligible ohmic resistance. The opposite graph shows how the current (I) in the two coils changes with time (t). The ratio between the self-inductances of the two coils $\left(\frac{L_x}{L_y}\right)$ equals ..........

1. A $\dfrac{1}{4}$
2. B $\dfrac{1}{2}$
3. C 2
4. D 4

In the circuit shown, three coils $L_1$, $L_2$, $L_3$, far apart and of no ohmic resistance, are connected together in parallel. Their self-inductances are 0.6 H, 0.2 H and 0.3 H, respectively. The inductive reactance of the group is ..........

1. A 0.1 Ω
2. B 6.28 Ω
3. C 31.4 Ω
4. D 100 Ω

In the circuit shown, the coils are identical with negligible ohmic resistance, and the self-inductance of each is 0.3 H. If their total inductive reactance is 12.56 Ω, and mutual induction between them is neglected, the frequency of the current in the circuit equals .......... (given that π = 3.14)

1. A 50 Hz
2. B 60 Hz
3. C 20 Hz
4. D 10 Hz

The circuit in front of you has five inductors. If the self-inductance of each is 50 mH, the total self-inductance between points A and B is ..........

1. A 50 mH
2. B 100 mH
3. C 150 mH
4. D 200 mH

In the circuit shown, the total inductive reactance is ..........

1. A 354.3 Ω
2. B 251.4 Ω
3. C 125.7 Ω
4. D 83.8 Ω

In the circuit shown, if the current in the circuit is 0.5 A, then $L_1$ equals ..........

1. A 0.6 H
2. B 0.9 H
3. C 1.8 H
4. D 1.9 H

The opposite circuit consists of inductors of no ohmic resistance and an AC source. The currents in the coils $L_2$ and $L_3$ are, respectively, .......... (given that π = 3.14)

1. A 20 A, 20 A
2. B 80 A, 20 A
3. C 80 A, 40 A
4. D 80 A, 80 A

A group of identical inductors, far apart, is connected in series to an AC source of frequency 50 Hz, and their equivalent inductive reactance is 50 Ω. If the same coils are connected in parallel to the same source, their equivalent inductive reactance is 2 Ω, then:
(1) The number of coils equals ..........

1. A 10
2. B 6
3. C 5
4. D 4

A group of identical inductors, far apart, is connected in series to an AC source of frequency 50 Hz, and their equivalent inductive reactance is 50 Ω. If the same coils are connected in parallel to the same source, their equivalent inductive reactance is 2 Ω, then:
(2) The inductive reactance of one coil is ..........

1. A 5 Ω
2. B 8 Ω
3. C 10 Ω
4. D 12.5 Ω

A group of identical inductors, far apart, is connected in series to an AC source of frequency 50 Hz, and their equivalent inductive reactance is 50 Ω. If the same coils are connected in parallel to the same source, their equivalent inductive reactance is 2 Ω, then:
(3) The self-inductance of each coil is about ..........

1. A 0.039 H
2. B 0.032 H
3. C 0.018 H
4. D 0.02 H

If a capacitor of capacitance 1 μF is connected to a DC voltage source, its capacitive reactance equals ..........

1. A zero
2. B ∞
3. C 1 Ω
4. D $\dfrac{1}{2}$ Ω

If the capacitance of a capacitor is 3 μF and the potential difference between its plates is 1 V, the charge stored on one of its plates is ..........

1. A 3 mC
2. B 0.03 mC
3. C 0.003 mC
4. D 0.333 mC

In the circuit shown in the figure, after closing switch K and the capacitor is fully charged, .......... (given that $e = 1.6 \times 10^{-19}$ C)

1. A type of charge on plate (y): negative, number of electrons on plate (x): $1.25 \times 10^{14}$
2. B type of charge on plate (y): negative, number of electrons on plate (x): $2.5 \times 10^{14}$
3. C type of charge on plate (y): positive, number of electrons on plate (x): $1.25 \times 10^{14}$
4. D type of charge on plate (y): positive, number of electrons on plate (x): $2.5 \times 10^{14}$

The quantity $\sqrt{\frac{L}{C}}$ has the same unit as .......... (where (L) is the self-inductance of the coil and (C) is the capacitance of the capacitor)

1. A resistance
2. B time
3. C frequency
4. D potential difference

The quantity (CR) is measured in .......... (where (C) is the capacitance of the capacitor and (R) is the ohmic resistance)

1. A ohm
2. B volt
3. C second
4. D hertz

In the circuit shown, at the moment switch K is closed, the current in the circuit ..........

1. A increases with time
2. B decreases then increases
3. C becomes zero when the capacitor is fully charged
4. D increases and decreases following a sine curve

Four capacitors x, y, z, k are connected together in parallel to a DC source of adjustable voltage. The opposite graph shows the relation between the charge (Q) on each capacitor and the potential difference (V) between its plates. Which of these capacitors has the largest capacitance?

1. A x
2. B y
3. C z
4. D k

Figure (1) shows the graph of the electric charge (Q) stored on the plates of each of three capacitors x, y, z against the potential difference (V) between its plates. If the three capacitors are connected as in figure (2), the equivalent capacitance between points a and b equals ..........

1. A 6 μF
2. B 8 μF
3. C 10 μF
4. D 12 μF

Two capacitors of capacitances $C_1$ and $C_2$: when connected in series their total capacitance is 2 μF, and when connected in parallel their total capacitance is 9 μF. The capacitances $(C_1)$ and $(C_2)$ are ..........

1. A 4 μF, 5 μF
2. B 3 μF, 6 μF
3. C 4 μF, 4 μF
4. D 2 μF, 9 μF

In the opposite figure, if the capacitance of each capacitor is 1 pF, the total capacitance is ..........

1. A 4 pF
2. B 3 pF
3. C $\dfrac{1}{2}$ pF
4. D $\dfrac{2}{5}$ pF

In the opposite figure, if the capacitance of each capacitor is C, the total capacitance is ..........

1. A 1.5 C
2. B 3 C
3. C $\dfrac{2}{3}$ C
4. D C

Three capacitors $C_1$, $C_2$, $C_3$ are connected together in parallel, and the group is connected across a battery. If $(C_3 > C_2 > C_1)$ and the charges stored on the plates of the capacitors are $Q_1$, $Q_2$, $Q_3$, respectively, then ..........

1. A $Q_3 > Q_2 > Q_1$
2. B $Q_1 > Q_3 > Q_2$
3. C $Q_1 > Q_2 > Q_3$
4. D $Q_1 = Q_2 = Q_3$

In the opposite figure, several capacitors each of capacitance 24 pF. The total capacitance of the group equals ..........

1. A 4.8 pF
2. B 16.8 pF
3. C 20 pF
4. D 24 pF

You have a group of identical capacitors, each of capacitance 15 μF. The connection that gives an equivalent capacitance of 10 μF is ..........

1. A A
2. B B
3. C C
4. D D

A group of capacitors has a total capacitance of 48 μF. It is required to decrease the total capacitance to 30 μF by adding a capacitor to this group. The capacitance of the capacitor to be added and how it is connected are ..........

1. A 64 μF, in series
2. B 80 μF, in series
3. C 64 μF, in parallel
4. D 80 μF, in parallel

The opposite figure shows four capacitors connected together by four switches. Which of these switches, when opened, decreases the total capacitance by 1.5 μF?

1. A $K_1$
2. B $K_2$
3. C $K_3$
4. D $K_4$

The opposite figure shows two capacitors x and y connected in series. Which of the following graphs shows the ratios of the potential differences across each of them when they are connected to an AC source?

1. A A
2. B B
3. C C
4. D D

Three capacitors (x), (y), (z) of capacitances C, 2 C and $\frac{1}{2}$ C, respectively, are connected together and to a DC voltage as in the opposite figure. The correct order of the three capacitors according to the charge on each is ..........

1. A $y > x > z$
2. B $z > x > y$
3. C $z = y > x$
4. D $z > y > x$

In the circuit shown, a DC source of 120 V is connected to three capacitors x, y, z, then:
(1) The potential differences across capacitors x and z, respectively, are ..........

1. A 120 V, 60 V
2. B 40 V, 80 V
3. C 80 V, 40 V
4. D 60 V, 20 V

In the circuit shown, a DC source of 120 V is connected to three capacitors x, y, z, then:
(2) The charges stored on capacitors x and y, respectively, are ..........

1. A 240 μC, 80 μC
2. B 120 μC, 160 μC
3. C 80 μC, 120 μC
4. D 160 μC, 120 μC

A circuit consists of several capacitors of different capacitances connected to a source of negligible internal resistance, as shown in the figure. Which of these capacitors stores the largest charge?

1. A $C_1$
2. B $C_2$
3. C $C_3$
4. D $C_4$

Two uncharged capacitors are connected to a battery of emf 24 V as in the opposite circuit. When switch (S) is put in position (1) until capacitor $C_1$ is fully charged, then put in position (2), the potential difference across capacitor $C_1$ becomes ..........

1. A 5 V
2. B 10 V
3. C 20 V
4. D 15 V

A charged capacitor of capacitance $C_1$ is connected to an uncharged capacitor of capacitance 3 $C_1$ through a switch K as in the figure. When switch K is closed, the charge of capacitor $C_1$ ..........

1. A doubles
2. B decreases to one half
3. C decreases to one third
4. D decreases to one quarter

Two charged capacitors (x) and (y) of capacitances C and 2 C, respectively, with equal potential differences across them, are connected to each other through a switch (K) as in the opposite figure. What happens to the potential difference across each of capacitors (x) and (y), respectively, after closing switch (K)?

1. A does not change, does not change
2. B decreases, decreases
3. C increases, decreases
4. D decreases, increases

Two charged capacitors (x) and (y) of capacitances C and 2 C, with potential differences 1 V and 2.5 V, respectively, are connected through a switch as in the opposite figure. After closing the switch, the potential difference across capacitor (x) ..........

1. A stays 1 V
2. B becomes 2 V
3. C becomes 3 V
4. D becomes 4 V

In the circuit shown in the opposite figure, the charge stored on the capacitor is ..........

1. A 5 μC
2. B 10 μC
3. C 15 μC
4. D 20 μC

Three capacitors (x), (y), (z) of capacitances C, 2 C and 4 C, respectively, are connected in a circuit as in the opposite figure. The correct order of the capacitors according to the potential difference across each is ..........

1. A $V_x > V_y > V_z$
2. B $V_x < V_y < V_z$
3. C $V_x = V_y = V_z$
4. D $V_x > V_z > V_y$

In the circuit shown in the figure:
(1) The values of $I_1$ and $I_3$, respectively, are ..........

1. A 3 A, 2 A
2. B 0.75 A, 0.75 A
3. C 1.25 A, 0.5 A
4. D 1.25 A, 1.25 A

In the circuit shown in the figure:
(2) The charge stored on one plate of the capacitor equals ..........

1. A 0.125 μC
2. B 0.5 μC
3. C 3.2 μC
4. D 5.5 μC

The opposite circuit contains two charged capacitors $C_1$ and $C_2$ of capacitances C and 2 C, respectively. The ratio between the charges on the two capacitors $\left(\frac{Q_1}{Q_2}\right)$ equals ..........

1. A $\dfrac{1}{2}$
2. B $\dfrac{3}{5}$
3. C $\dfrac{1}{1}$
4. D $\dfrac{3}{10}$

In the circuit shown in the figure, if the voltage lags behind the current in phase, the element (X) is ..........

1. A a capacitor
2. B an ohmic resistance
3. C an inductor of negligible ohmic resistance
4. D a hot-wire ammeter

The terminals of an AC source are connected to three electrical components (x), (y), (z), each on its own. The following graphs show how the potential difference (V) across the source and the current (I) in it change with time (t). The components (x), (y), (z) are ..........

1. A (x): non-inductive resistance, (y): capacitor, (z): inductor of no resistance
2. B (x): non-inductive resistance, (y): inductor of no resistance, (z): capacitor
3. C (x): inductor of no resistance, (y): capacitor, (z): non-inductive resistance
4. D (x): inductor of no resistance, (y): non-inductive resistance, (z): capacitor

A capacitor of fixed capacitance is connected directly to an AC source of frequency f, and its capacitive reactance is $X_C$. If the frequency of the current is tripled, its capacitive reactance ..........

1. A triples
2. B becomes nine times as large
3. C decreases to one third
4. D stays the same

The opposite graph shows the relation between the capacitive reactance $(X_C)$ of a variable capacitor connected to an AC voltage source of frequency f and the reciprocal of the capacitance $\left(\frac{1}{C}\right)$. The frequency f of the current equals ..........

1. A 52.55 Hz
2. B 64.54 Hz
3. C 79.55 Hz
4. D 81.48 Hz

The opposite graph shows the relation between the capacitive reactance $(X_C)$ of two capacitors of capacitances $C_1$ and $C_2$ and the frequency (f). The relation between them is ..........

1. A $C_1 = C_2$
2. B $C_1 > C_2$
3. C $C_1 < C_2$
4. D cannot be determined

An AC source whose frequency can be changed while its effective voltage stays constant is connected to a capacitor of capacitance C, as shown in the figure. Which of the following graphs shows the relation between the effective current in the circuit $(I_{eff})$ and the angular frequency (ω) of the source?

1. A A
2. B B
3. C C
4. D D

A circuit consists of an AC dynamo of negligible internal resistance and a capacitor. The graph that shows the relation between the maximum alternating current $(I_{max})$ in the circuit and the frequency (f) of rotation of the dynamo coil is ..........

1. A A
2. B B
3. C C
4. D D

A capacitor of capacitance $\frac{7000}{11}$ μF is connected to an AC source of 20 V and frequency 50 Hz, then:
(1) The capacitive reactance of the capacitor equals ..........

1. A 0.1 Ω
2. B 0.2 Ω
3. C 5 Ω
4. D 10 Ω

A capacitor of capacitance $\frac{7000}{11}$ μF is connected to an AC source of 20 V and frequency 50 Hz, then:
(2) The current in the circuit is ..........

1. A 1 A
2. B 2 A
3. C 3 A
4. D 4 A

The opposite figure shows two circuits, each containing an AC source and a capacitor. If $\frac{(X_C)_1}{(X_C)_2} = \frac{2}{3}$, then ..........

1. A $\dfrac{C_1}{C_2} = \dfrac{3}{4}$
2. B $\dfrac{C_1}{C_2} = \dfrac{6}{1}$
3. C $\dfrac{C_1}{C_2} = \dfrac{8}{3}$
4. D $\dfrac{C_1}{C_2} = \dfrac{1}{12}$

A capacitor of capacitance $\frac{700}{22}$ μF is connected across an AC source whose instantaneous voltage is given by $V = 100 \sin (200 \pi t)$. The instantaneous current in the circuit is given by ..........

1. A $I = 2 \sin (200 \pi t)$
2. B $I = 0.5 \sin \left(200 \pi t + \dfrac{\pi}{2}\right)$
3. C $I = 2 \sin \left(200 \pi t - \dfrac{\pi}{2}\right)$
4. D $I = 2 \sin \left(200 \pi t + \dfrac{\pi}{2}\right)$

In the figure shown, if all capacitors have the same capacitance and the total capacitive reactance is 50 Ω, the capacitance of each capacitor C equals .......... (given that π = 3.14)

1. A 2 μF
2. B 6 μF
3. C 12 μF
4. D 30 μF

An AC source of effective voltage 500 V and frequency $\frac{100}{\pi}$ Hz is connected to a group of capacitors as in the opposite figure, and an effective current of 2 A passes in the circuit. The capacitance C equals ..........

1. A 15 μF
2. B 10 μF
3. C 20 μF
4. D 50 μF

Three capacitors, each of capacitance 14 μF, are connected together in parallel and to a source of frequency 50 Hz. The total capacitive reactance is ..........

1. A 681.8 Ω
2. B 322.3 Ω
3. C 151.5 Ω
4. D 75.76 Ω

Three capacitors of 10, 20 and 30 microfarad are connected in series to a source of emf 200 volt and frequency 42 hertz, then:
(1) The total capacitive reactance equals ..........

1. A 1388.8 Ω
2. B 695.02 Ω
3. C 126.26 Ω
4. D 63.13 Ω

Three capacitors of 10, 20 and 30 microfarad are connected in series to a source of emf 200 volt and frequency 42 hertz, then:
(2) The current in the circuit is ..........

1. A 3.16 A
2. B 1.58 A
3. C 0.29 A
4. D 0.14 A

An AC source of 400 V and frequency 50 Hz is connected to a group of capacitors as in the opposite figure. The total current through the source equals ..........

1. A 0.94 A
2. B 2.03 A
3. C 4.02 A
4. D 5.03 A

From the opposite figure, ..........

1. A $V_1$: 12 V, $V_2$: 5 V, $V_3$: 5 V
2. B $V_1$: 10 V, $V_2$: 8 V, $V_3$: 4 V
3. C $V_1$: 12 V, $V_2$: 6 V, $V_3$: 4 V
4. D $V_1$: 4 V, $V_2$: 6 V, $V_3$: 12 V

The opposite graph shows how the emf (V) induced in a dynamo coil changes with time (t). If the terminals of this dynamo are connected to a capacitor of capacitance 2 μF, the effective current through the source is ..........

1. A 0.445 A
2. B 0.314 A
3. C 0.22 A
4. D 0.15 A

A dynamo coil of 100 turns and area 0.05 m² is in a uniform magnetic field of flux density 0.225 T. The terminals of this coil are connected to a capacitor of capacitive reactance 1 kΩ, and an effective current of 0.25 A passes in the circuit. The angular frequency of the dynamo coil is about ..........

1. A 157 rad/s
2. B 314 rad/s
3. C 471 rad/s
4. D 628 rad/s

An AC source of negligible internal resistance has its terminals connected to a pure element. The opposite graph shows the current (I) in the circuit and the potential difference (V) across the source against time (t). The electric power consumed in the circuit equals ..........

1. A $I_{max} V_{max}$
2. B $\dfrac{I_{max} V_{max}}{2}$
3. C $\dfrac{I_{max} V_{max}}{\sqrt{2}}$
4. D zero

Give a reason: measuring the value of an alternating current depends on its heating effect.

The opposite figure shows an electric circuit containing two ammeters A₁ and A₂ of two different types. When switch K is closed:
(1) What type of energy is the electrical energy changed into, causing the pointer to deflect, in each of the two instruments?
(2) Which of the two ammeters has its pointer settle first at a definite reading? Why?
(3) In which of the two instruments: (a) does an electric current pass through the spring? (b) does the spring cause the pointer to deflect from zero?

When a hot-wire ammeter is used to measure a direct current, does its scale need to be calibrated to be uniform before measuring? Why?

A student wanted to use a hot-wire ammeter to measure the current in a circuit, but he noticed that the pointer of the ammeter rests at a reading of 1 A before any current passes through it, as in the opposite figure:
(1) What is the likely reason why the pointer does not rest at zero although no current passes through the ammeter?
(2) The student thought of passing the current in the circuit, recording the reading where the pointer settles, then subtracting 1 A from it to correct the zero error. Is this idea scientifically accurate? Why?
(3) What solutions do you suggest to stop the pointer from resting away from zero before the current passes?

In the circuit shown in the figure, all coils have no ohmic resistance. The current in coil z is twice the current in coil x and half the current in coil y. Calculate the self-inductances of coils x and y.

An AC circuit consists of three coils of negligible ohmic resistance, an AC source and a switch K, as in the opposite figure. What happens, when switch K is closed, to:
(1) the phase difference between the total voltage and the current in the circuit?
(2) the potential difference across coil z?
(3) the current in coil x?

In the opposite circuit, all coils have no ohmic resistance:
(1) Find the potential difference between points: (a) a and c (b) b and d
(2) If the current in the circuit is 1 A, find the self-inductance L.

What is the result of winding the wires of a solenoid carrying an alternating current as a double (non-inductive) winding, regarding the inductive reactance of the coil?

Prove that the quantity L/R has the same unit as time, where (L) is the self-inductance of the coil and (R) is the ohmic resistance.

In the opposite circuit, all coils have negligible ohmic resistance. What happens to the maximum current in coil L₁ when:
(1) switch K is closed?
(2) the frequency of the source is increased?

The opposite figure shows an AC dynamo whose coil has negligible ohmic resistance and rotates with frequency f. Its terminals are connected to an inductor (L) of negligible ohmic resistance. What happens to the current in the dynamo coil when:
(1) the turns of coil (L) are brought closer to each other uniformly?
(2) another coil (L) is connected in series in the external circuit?
(3) the speed of rotation of the dynamo coil is increased?
(4) an iron core is placed inside the coil?
(5) the dynamo coil is replaced by another one with twice the number of turns of the first coil?

The following figure shows three electric circuits (1), (2), (3), each with a capacitor of capacitance C, a 20 V source and a hot-wire ammeter. Explain each of the following:
(1) The reading of ammeter A₃ is zero while the readings of ammeters A₁ and A₂ are not zero.
(2) The reading of ammeter A₁ is greater than the reading of ammeter A₂

In the opposite circuit, a capacitor C, a battery V_B of negligible internal resistance and a switch K are connected together in series. When switch K is closed, capacitor C takes a time t to be fully charged. Describe what happens during the time t to:
(1) the rate of flow of electric charge from the battery to the capacitor.
(2) the potential difference between the plates of the capacitor.
(3) the potential difference between the terminals of the battery.

Three capacitors C₁, C₂, C₃ are connected in series as in the opposite figure, and plate x of capacitor C₁ carries a positive charge Q. Find the type and amount of charge on plates y and z.

In the opposite figure, what type of electric charge forms on plate A of the capacitor while the magnet is moved towards the metal ring? Why?

Three capacitors of different capacitances C₁, C₂, C₃ are connected in parallel to a DC source of voltage V. Prove that the charge stored on each capacitor differs from one capacitor to another after they are fully charged.

Two capacitors a and b of different capacitances, because their plates have different areas, are connected in series with a battery as in the opposite figure. Does the charge stored on the plates of the two capacitors differ? Why?

The circuit shown in the opposite figure was used to find the capacitance of capacitor (C), where the potential difference applied between the plates of the capacitor changes by moving the slider d along the wire ab:
(1) Draw a graph of the charge (Q) stored on the capacitor on the vertical axis against the potential difference (V) between its plates on the horizontal axis.
(2) How can the capacitance (C) be found from the graph?

A group of four capacitors C₁, C₂, C₃, C₄ is connected to a DC source as in the opposite figure. If the charge of capacitor C₁ equals the charge of capacitor C₃, find the capacitance of capacitor C₄

In the opposite circuit, if the effective alternating current in the circuit is 1 A, calculate:
(1) the capacitance of the capacitor (C).
(2) the effective emf of the source (V_eff), neglecting its internal resistance.

In the opposite circuit, when the capacitance of capacitor C₁ is increased, what happens to:
(1) the phase difference between the total voltage and the current in the circuit?
(2) the current through the source?
(3) the potential difference between the plates of capacitor C₂?

In the circuit shown in the figure, neglecting the ohmic resistance in the circuit, calculate the ratio between the currents in the circuit before and after closing the switch (I₁/I₂).

Write the mathematical relation shown by each graph, and what the slope of the straight line equals, for each of the following:
where: (X_L) is the inductive reactance of the coil, (ω) the angular velocity, (X_C) the capacitive reactance of a capacitor, (f) the frequency, (C) the capacitance of the capacitor.

The wire of a hot-wire ammeter is fixed on a metal plate with the same thermal expansion coefficient, in order to .......... (Trial exam / May 2021)

1. A return the pointer quickly to zero when the current is cut off
2. B decrease the efficiency of the instrument in measuring
3. C get rid of the zero error
4. D increase the thermal expansion of the wire

When calibrating the scale of a hot-wire ammeter, its pointer deflected as in the opposite figure when an alternating current of effective value I passed. Which of the following figures correctly shows the position of the pointer when an alternating current of effective value 2I passes through the ammeter? (Trial exam / June 2021)

1. A A
2. B B
3. C C
4. D D

Some students drew a diagram of a hot-wire ammeter. Which student drew the scale of the hot-wire ammeter correctly? (1st session 2021)

1. A student (A)
2. B student (B)
3. C student (C)
4. D student (D)

In a hot-wire ammeter, the amount of heat produced in the platinum-iridium wire by an alternating current is directly proportional to .......... (2nd session 2021)

1. A $\frac{1}{V_{eff}^2}$
2. B $I_{eff}$
3. C $I_{max}$
4. D $V_{eff}^2$

In a hot-wire ammeter, the pointer moves over a scale with unequal divisions because .......... (1st session 2022)

1. A the hot-wire ammeter measures the maximum value of the alternating current
2. B the pointer of the hot-wire ammeter moves slowly when the current starts
3. C the amount of heat produced is directly proportional to the current
4. D the amount of heat produced is directly proportional to the square of the current

In a country with a very hot climate, a student wanted to use the hot-wire ammeter in the school lab, which is not air-conditioned. Which two figures correctly show the position of the pointer of the hot-wire ammeter at the lab temperature? (2nd session 2022)
(given that XY is a strip of a material with the same expansion coefficient as the platinum-iridium wire)

1. A figures 2 and 4
2. B figures 1 and 3
3. C figures 2 and 3
4. D figures 1 and 4

The figure shows the scale of a hot-wire ammeter, and the distances between the divisions in the figure are equal. If a current I passes through the wire of the instrument, the pointer deflects to division V. Which of the following choices is the current in the wire when the pointer deflects to division Y? (Trial exam 2023)

1. A 2I
2. B 3I
3. C 4I
4. D 5I

In a hot-wire ammeter, when the shunt is decreased while the effective current in the circuit stays constant, .......... (1st session 2023)

1. A the heat power produced in the platinum-iridium wire: decreases, the total resistance of the ammeter: increases
2. B the heat power produced in the platinum-iridium wire: decreases, the total resistance of the ammeter: decreases
3. C the heat power produced in the platinum-iridium wire: increases, the total resistance of the ammeter: decreases
4. D the heat power produced in the platinum-iridium wire: increases, the total resistance of the ammeter: increases

An electric current (I) passes through the wire of a hot-wire ammeter. When the current through the wire is increased to (2I), .......... (2nd session 2023)

1. A the expansion of the wire: increases, the heat energy produced in the wire per unit time: doubles
2. B the expansion of the wire: decreases, the heat energy produced in the wire per unit time: decreases to one half
3. C the expansion of the wire: increases, the heat energy produced in the wire per unit time: becomes 4 times as large
4. D the expansion of the wire: decreases, the heat energy produced in the wire per unit time: decreases to one quarter

The following diagrams show attempts by some students to show the structure of a hot-wire ammeter. Which of these figures shows the correct structure of the hot-wire ammeter? (1st session 2024)

1. A (1)
2. B (2)
3. C (3)
4. D (4)

In a hot-wire ammeter, when the shunt is replaced by another of a smaller value while the effective current in the circuit stays constant, .......... (2nd session 2024)

1. A the heat power produced in the platinum-iridium wire: increases, the total resistance of the ammeter: increases
2. B the heat power produced in the platinum-iridium wire: decreases, the total resistance of the ammeter: decreases
3. C the heat power produced in the platinum-iridium wire: increases, the total resistance of the ammeter: decreases
4. D the heat power produced in the platinum-iridium wire: decreases, the total resistance of the ammeter: increases

The opposite graph shows the relation between a direct current (I) and time (t). Which of the following graphs shows the alternating current that gives the same heat energy in the same resistance in the same time as the direct current? (2nd session 2024)

1. A A
2. B B
3. C C
4. D D

The opposite figure shows two deflections of the pointer of a hot-wire ammeter from zero. The value of θ₁ in terms of θ equals .......... (Sample exam 2025)

1. A $5\theta$
2. B $10\theta$
3. C $15\theta$
4. D $20\theta$

Alternating current cannot be used directly for .......... (Sample exam 2025)

1. A lighting lamps
2. B running household appliances
3. C charging batteries
4. D operating electric transformers

When an alternating current of effective value (I) passes through a hot-wire ammeter, the electric power consumed in the platinum-iridium wire is ($P_w$). The effective value of the alternating current that makes the power consumed in the same hot-wire ammeter ($2P_w$) equals .......... (Sample exam 2025)

1. A $I$
2. B $\sqrt{2}\,I$
3. C $0.5\,I$
4. D $2I$

In a hot-wire ammeter, when the platinum-iridium wire is replaced by another wire of a metal with a smaller thermal expansion coefficient and the same current passes through it, the deflection angle of the pointer .......... (Sample exam 2025)

1. A increases
2. B decreases
3. C does not change
4. D becomes zero

The opposite figure shows the scale of a hot-wire ammeter and several values of the current, where:
($\Delta I_1$) is the change in current from zero to position X
($\Delta I_2$) is the change in current from position X to position Y
($\Delta I_3$) is the change in current from position Y to position Z
If the angles shown are equal, the correct order of the changes in current is .......... (Sample exam 2025)

1. A $\Delta I_1 > \Delta I_2 > \Delta I_3$
2. B $\Delta I_1 = \Delta I_2 = \Delta I_3$
3. C $\Delta I_1 < \Delta I_2 < \Delta I_3$
4. D $\Delta I_1 < \Delta I_2 > \Delta I_3$

Which of the following graphs shows the relation between the amount of heat (Q) produced in the (platinum-iridium) wire and the current in it (I)? (Sample exam 2025)

1. A A
2. B B
3. C C
4. D D

The reading of a hot-wire ammeter in an AC circuit represents .......... (1st session 2025)

1. A the average value over a complete cycle of the alternating current
2. B the maximum value of the alternating current
3. C the instantaneous value of the alternating current
4. D the effective value of the alternating current

The figure shows an electric circuit consisting of a DC source, a variable resistance (R), a hot-wire ammeter (H) and a moving-coil ammeter (M). If the current changes by equal amounts, what happens to the pointer of each ammeter? (2nd session 2025)

1. A ammeter (H): deflects by equal angles, ammeter (M): deflects by equal angles
2. B ammeter (H): deflects by equal angles, ammeter (M): deflects by unequal angles
3. C ammeter (H): deflects by unequal angles, ammeter (M): deflects by equal angles
4. D ammeter (H): deflects by unequal angles, ammeter (M): deflects by unequal angles

Four different electric circuits each contain a hot-wire ammeter. Each of the following graphs w, x, y, z shows the current (I) through the ammeter against time (t). The correct order of the graphs according to the reading of the hot-wire ammeter is .......... (Sample exam 2026)

1. A $z < x < y < w$
2. B $w < z < y < x$
3. C $x < y < z < w$
4. D $x < y = z < w$

The following figures show four electric circuits, each with a resistance R, and the sources in each have negligible ohmic resistance. The circuit in which the power consumed is the largest is .......... (Sample exam 2025)

1. A A
2. B B
3. C C
4. D D

The figure shows inductors of no ohmic resistance connected to an AC source. The voltage of the AC source equals .......... (1st session 2023)

1. A 20 V
2. B 40 V
3. C 120 V
4. D 80 V

The following figure shows two AC circuits, one containing an ohmic resistance (R) and the other an inductor (L) of no ohmic resistance. If the voltages of the two sources are in phase, the phase difference between the two currents $I_L$ and $I_R$ is shown by figure .......... (Trial exam / May 2021)

1. A A
2. B B
3. C C
4. D D

The figure shows an AC source whose instantaneous voltage is given by $V = 200\sin(100\pi t)$, connected to an inductor (X) of self-inductance L and no ohmic resistance. If the effective current in the circuit is 2 A, what is the self-inductance of another coil of no ohmic resistance connected with coil (X) so that the effective current in the circuit doubles? And how is it connected with coil (X)? (Trial exam / May 2021, Sample exam 2025)

1. A 0.22 H, in series
2. B 0.22 H, in parallel
3. C 0.11 H, in series
4. D 0.11 H, in parallel

Three inductors of negligible ohmic resistance are connected together as in the figure. If the effective current in the circuit is 5 A, and mutual induction between these coils is neglected, then L equals .......... (Trial exam / June 2021)

1. A 0.6 H
2. B 0.4 H
3. C 0.3 H
4. D 0.2 H

A number of identical inductors of negligible ohmic resistance are connected together in series to an AC source of frequency $\frac{50}{\pi}$ Hz, and their total inductive reactance is 40 Ω. When they are connected together in parallel to the same source, their total inductive reactance is 2.5 Ω. Neglecting mutual induction between the coils, the self-inductance of each coil equals .......... (1st session 2021)

1. A 0.1 H
2. B 0.2 H
3. C 0.3 H
4. D 0.4 H

Four inductors of negligible ohmic resistance, each of self-inductance 50 mH, are connected together as in the opposite circuit. If the effective current in the circuit is 10 A, and mutual induction between the coils is neglected, the frequency of this current is about .......... (2nd session 2021)

1. A 20 Hz
2. B 50 Hz
3. C 10 Hz
4. D 60 Hz

Two electric circuits A and B as in the figure. The total inductive reactance of circuit A equals .......... and the total inductive reactance of circuit B equals .......... (π = 3.14) (1st session 2022)

1. A circuit A: zero Ω, circuit B: 94.2 Ω
2. B circuit A: 125.6 Ω, circuit B: 94.2 Ω
3. C circuit A: zero Ω, circuit B: 62.8 Ω
4. D circuit A: 125.6 Ω, circuit B: 62.8 Ω

When an AC source (50 Hz, 220 V) is connected to a coil of self-inductance L and negligible ohmic resistance as in the figure, a current of 2 A passes through the coil. The self-inductance L is .......... (π = 3.14) (1st session 2022)

1. A 0.7 H
2. B 0.35 H
3. C 4.4 H
4. D 0.04 H

In the opposite circuit, the total inductive reactance equals .......... (2nd session 2022)

1. A 40 Ω
2. B 60 Ω
3. C 20 Ω
4. D 80 Ω

A coil of self-inductance (L) and negligible ohmic resistance is put in two AC circuits as shown in the figure. The ratio of the current of circuit (1) to the current of circuit (2) = .......... (2nd session 2022)

1. A $\frac{1}{1}$
2. B $\frac{2}{1}$
3. C $\frac{4}{1}$
4. D $\frac{1}{2}$

The figure shows an electric circuit containing two inductors connected to an AC source. The phase angle between the total voltage and the source current after closing switch K equals .......... (given that the ohmic resistance in the circuit is negligible) (Trial exam 2023)

1. A 180°
2. B 90°
3. C 45°
4. D zero

From the data shown in the figure, the effective current in the circuit equals .......... (given that the ohmic resistance in the circuit is negligible) (Trial exam 2023)

1. A 0.05 mA
2. B 0.5 mA
3. C 5 mA
4. D 50 mA

Three inductors of negligible ohmic resistance are connected to an AC source as in the figure. The self-inductance of coil (L) that lets a current of 3 A pass in the circuit is .......... (neglecting mutual induction between the coils) (2nd session 2023)

1. A 0.08 mH
2. B 80 mH
3. C 40 mH
4. D 120 mH

The opposite figure shows an electric circuit with several inductors connected together. The ratio of (the total inductive reactance when K₁ is closed and K₂ is open) to (the total inductive reactance when K₂ is closed and K₁ is open) = .......... (1st session 2024)

1. A $\frac{1}{3}$
2. B $\frac{2}{3}$
3. C $\frac{3}{1}$
4. D $\frac{3}{2}$

In the following two figures, neglecting the ohmic resistance of the coils and the mutual induction between them, the ratio between the currents through the two sources ($\frac{I_2}{I_1}$) = .......... (2nd session 2024)

1. A $\frac{20}{7}$
2. B $\frac{7}{20}$
3. C $\frac{20}{3}$
4. D $\frac{3}{20}$

If the potential difference (V) across an inductor of no ohmic resistance connected to an AC source changes with time (t) as in the opposite graph, the graph that shows how the current (I) in the coil changes with time (t) during the same period is .......... (Sample exam 2025)

1. A A
2. B B
3. C C
4. D D

If the inductive reactance of a coil = (440 L) ohm, where (L) is the self-inductance of the coil, the angular velocity is .......... (Sample exam 2025)

1. A 440 rad/s
2. B 140 rad/s
3. C 70 rad/s
4. D 80 rad/s

The figure shows an AC circuit consisting of an AC source, an ohmic resistance (R) and an inductor (L) of negligible ohmic resistance. What is the phase angle between the voltage across the source and the current in the circuit in the following two cases? (1st session 2025)

1. A only K₁ closed: 90°, only K₂ closed: 90°
2. B only K₁ closed: 0°, only K₂ closed: 90°
3. C only K₁ closed: 90°, only K₂ closed: 0°
4. D only K₁ closed: 0°, only K₂ closed: 0°

Two AC circuits: circuit (1) consists of an AC source and an ohmic resistance, and circuit (2) consists of an AC source and an inductor of negligible ohmic resistance. Which of the following choices shows the phase angle between the total voltage and the current in each circuit? (2nd session 2025)

1. A A
2. B B
3. C C
4. D D

The figure shows an AC source of frequency (f) connected to several inductors of no ohmic resistance. If the current in coil (3L) is (I), the potential difference between points a and b equals .......... (Sample exam 2026)

1. A $4I\pi Lf$
2. B $2I\pi Lf$
3. C $\frac{1}{2}I\pi Lf$
4. D $\frac{1}{4}I\pi Lf$

A capacitor of capacitance 10 µF is connected to an oscillator of frequency 1000 Hz with a maximum emf of 5 V. The maximum current in the capacitor circuit is about .......... (Trial exam / May 2021)

1. A 0.6 A
2. B 1.2 A
3. C 0.8 A
4. D 0.3 A

In the two circuits shown, if the capacitance of each capacitor is (C), the ratio of (the equivalent capacitive reactance in circuit (1)) to (the equivalent capacitive reactance in circuit (2)) equals .......... (Trial exam / June 2021)

1. A $\frac{1}{2}$
2. B $\frac{2}{1}$
3. C $\frac{8}{1}$
4. D $\frac{1}{8}$

The figure shows a circuit containing an AC voltage source, a hot-wire ammeter of negligible ohmic resistance and a capacitor. The reading of the hot-wire ammeter is .......... (Trial exam / June 2021)

1. A 0.02 A
2. B 0.2 A
3. C 2 A
4. D 20 A

The opposite figure shows an electric circuit containing a hot-wire ammeter of negligible ohmic resistance, a capacitor and an AC source. The effective voltage of the source is .......... (1st session 2021)

1. A 2.5 V
2. B 250 V
3. C 25 V
4. D 2500 V

The following figures show four equal capacitors, each of capacitance (C). Which figure should be connected between points a and b to close the circuit shown so that the current is as large as possible? (1st session 2021)

1. A A
2. B B
3. C C
4. D D

In the two circuits shown, if the capacitance of each capacitor is (C), the ratio of (the capacitive reactance in circuit (2)) to (the capacitive reactance in circuit (1)) = .......... (2nd session 2021)

1. A $\frac{2}{1}$
2. B $\frac{1}{4}$
3. C $\frac{4}{1}$
4. D $\frac{1}{2}$

The following figures show four different ways of connecting three capacitors, each of capacitance (C). Which figure should be connected between points a and b to close the circuit shown so that the current is as small as possible? (1st session 2022)

1. A figure (1)
2. B figure (2)
3. C figure (3)
4. D figure (4)

The opposite figure shows two capacitors connected in series, each of capacitance (C). When another capacitor, whose capacitance is half that of one of the two capacitors, is connected in parallel between points A and B, the total capacitance of the three capacitors equals .......... (2nd session 2022)

1. A C
2. B 2C
3. C $\frac{C}{2}$
4. D $\frac{3}{2}C$

The graph shows the alternating current (I) in a circuit containing a capacitor against time (t). Which of the following graphs shows the potential difference (V) across the plates of the capacitor against time (t) during the same period? (Trial exam 2023)

1. A A
2. B B
3. C C
4. D D

In the circuit shown in the figure, the ratio between the capacitances of the group of capacitors before and after closing switch (K), respectively, is .......... (Trial exam 2023)

1. A $\frac{7}{11}$
2. B $\frac{11}{7}$
3. C $\frac{6}{1}$
4. D $\frac{1}{6}$

The figure shows two capacitors (1) and (2). Capacitor (1) is charged with 60 µC and capacitor (2) is uncharged. Which of the following choices gives the final charge on each capacitor after closing switch (K)? (1st session 2023)

1. A $Q_1 = 40\ \mu C$ , $Q_2 = 20\ \mu C$
2. B $Q_1 = 20\ \mu C$ , $Q_2 = 40\ \mu C$
3. C $Q_1 = 30\ \mu C$ , $Q_2 = 30\ \mu C$
4. D $Q_1 = 0$ , $Q_2 = 60\ \mu C$

Three capacitors, each of (12 µF), are connected to a 20 V DC source in two different ways, as in figures (A, B). The ratio of the charge on each capacitor in circuit (A) to the charge on each capacitor in circuit (B) ($\frac{Q_A}{Q_B}$) is .......... (2nd session 2023)

1. A $\frac{9}{1}$
2. B $\frac{1}{9}$
3. C $\frac{3}{1}$
4. D $\frac{1}{3}$

The opposite figure shows part of an electric circuit. If the charge on one plate of capacitor ($C_3$) is 2.4 mC, the voltmeter (V) reads .......... (Sample exam 2025)

1. A 10 V
2. B 20 V
3. C 100 V
4. D 200 V

The figure shows an AC circuit consisting of an AC source and a group of capacitors. Using the data on the figure, the equivalent capacitive reactance of the circuit equals .......... (1st session 2025)

1. A $\frac{4.8}{\pi}\ k\Omega$
2. B $\frac{1}{\pi}\ k\Omega$
3. C $2\pi\ k\Omega$
4. D $\pi\ k\Omega$

An electric circuit consists of an AC source of frequency $\frac{100}{\pi}$ Hz and a group of identical capacitors, each of capacitance C. When the capacitors were connected together in series, the capacitive reactance of the circuit was 200 Ω, and when they were connected together in parallel, it was 12.5 Ω. The number of capacitors is .......... (2nd session 2025)

1. A 4 capacitors
2. B 8 capacitors
3. C 12 capacitors
4. D 16 capacitors