AC Circuits (continued) questions

In the opposite circuit, the AC source has a constant effective voltage and its frequency can be changed. The effective value of the current in the circuit increases when ..........

1. A the source frequency is increased
2. B the source frequency is decreased
3. C the resistance R is increased
4. D an iron core is put inside the coil

In the opposite circuit, when the iron rod gets inside the coil, the voltmeter reading ..........

1. A decreases
2. B increases
3. C increases then decreases
4. D stays constant

An AC circuit consists of an inductor, an ohmic resistor and an AC source, all connected in series. Which of the following graphs represents the relation between the impedance (Z) of the circuit and the frequency (f) of its current?

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

In the circuit shown in the figure, if the AC source is replaced by a DC source whose voltage equals the effective voltage of the AC source, the ratio of the effective current in the circuit in the first case to the current in the circuit in the second case is ..........

1. A zero
2. B less than one
3. C equal to one
4. D greater than one

In the opposite circuit, the total impedance Z equals ..........

1. A 2 Ω
2. B 48 Ω
3. C 14 Ω
4. D 10 Ω

An inductor has an ohmic resistance of 12 Ω. When a current of frequency f passes through it, its inductive reactance is 18 Ω, so:
(1) its total impedance in this case is ..........

1. A 20.1 Ω
2. B 16.3 Ω
3. C 21.6 Ω
4. D 36.2 Ω

An inductor has an ohmic resistance of 12 Ω. When a current of frequency f passes through it, its inductive reactance is 18 Ω, so:
(2) its total impedance when the frequency increases to 2 f is ..........

1. A 37.95 Ω
2. B 22 Ω
3. C 36 Ω
4. D 19.99 Ω

A circuit contains an AC source and a coil whose inductive reactance is twice its ohmic resistance. The phase angle between the total voltage and the current is ..........

1. A 26.56°
2. B 60°
3. C 30.7°
4. D 63.4°

In the circuit shown in the figure, when a current of frequency f passes, $(X_L = R)$ and the impedance of the circuit is $Z_1$. If the frequency increases to 2 f, the impedance of the circuit $Z_2$ becomes ..........

1. A $\dfrac{Z_1}{2}$
2. B 2 $Z_1$
3. C 1.6 $Z_1$
4. D 2.5 $Z_1$

An inductor has an ohmic resistance R and an inductive reactance $\sqrt{3}$ R when connected to an AC source of frequency f. The phase angle between the voltage across the coil and its current equals ..........

1. A $\dfrac{\pi}{3}$
2. B $\dfrac{\pi}{2}$
3. C $\dfrac{\pi}{4}$
4. D $\dfrac{\pi}{6}$

In the electric circuit shown in the opposite figure, if switch K is closed, the phase angle between the total voltage and the current in the circuit ..........

1. A decreases by 45°
2. B increases by 63.4°
3. C increases by 45°
4. D increases by 18.4°

An inductor of self-inductance L and ohmic resistance 10 Ω is connected to an AC source of voltage 6.5 V and frequency $\frac{30}{\pi}$ Hz. If the power consumed in the circuit is $\frac{5}{8}$ W, the self-inductance (L) of the coil equals ..........

1. A 1.1 H
2. B 0.3 H
3. C 0.4 H
4. D 0.6 H

An inductor of ohmic resistance 2 Ω is connected to an AC source of effective voltage 6 V. The inductive reactance of the coil is 1 Ω, so the power consumed in the circuit equals ..........

1. A 8 W
2. B 12 W
3. C 14.4 W
4. D 18 W

An electric lamp of ohmic resistance 44 Ω is connected in series with an inductor of negligible ohmic resistance and an AC source of frequency 42 Hz and effective emf 220 V. An effective current of 4 A passes through the lamp, so the self-inductance of the coil equals ..........

1. A 0.163 H
2. B 0.125 H
3. C 0.14 H
4. D 0.1 H

The opposite figure shows an AC circuit. When the potential difference across the coil equals the potential difference across the ohmic resistor, the source frequency equals ..........

1. A 50 Hz
2. B 100 Hz
3. C 200 Hz
4. D 400 Hz

An inductor of self-inductance 0.01 H and ohmic resistance 1 Ω is connected to an AC source of voltage 200 V and frequency 50 Hz. The maximum value of the current ..........

1. A lags behind the maximum value of the total voltage by 0.004 s
2. B leads the maximum value of the total voltage by 0.003 s
3. C lags behind the maximum value of the total voltage by 0.002 s
4. D leads the maximum value of the total voltage by 0.001 s

An AC generator (dynamo) of negligible internal resistance is connected in series with an ohmic resistor (R) and an inductor (L) of negligible ohmic resistance. When the dynamo frequency is 50 Hz, the maximum value of the total voltage leads the maximum value of the current by a time of $2.5 \times 10^{-3}$ s. If the dynamo frequency increases to 100 Hz, the maximum value of the total voltage ..........

1. A leads the maximum value of the current by $1.76 \times 10^{-3}$ s
2. B leads the maximum value of the current by $3.52 \times 10^{-3}$ s
3. C lags behind the maximum value of the current by $1.76 \times 10^{-3}$ s
4. D lags behind the maximum value of the current by $3.52 \times 10^{-3}$ s

In the circuit shown, if the reading of $V_1$ is 10 V, the reading of $V_2$ is ..........

1. A $10\sqrt{3}$ V
2. B 10 V
3. C 15 V
4. D $10\sqrt{2}$ V

An AC generator (dynamo) is connected to an ohmic resistor (R) and an inductor (L) of negligible ohmic resistance as shown in the opposite circuit. If the readings of the two voltmeters $(V_1)$ and $(V_2)$ are equal, which of the following relations is correct for the two readings after the rotation frequency of the dynamo coil is doubled?

1. A $V_1 = V_2$
2. B $V_1 > V_2$
3. C $V_1 < V_2$
4. D The answer cannot be determined

In the opposite figure, the total impedance of the circuit equals ..........

1. A 17 Ω
2. B 13 Ω
3. C 12.2 Ω
4. D 7 Ω

An inductor has a self-inductance of $\frac{7}{44}$ H and an inductive reactance of 50 Ω. If its ohmic resistance is 30 Ω, then:
(1) the frequency of the current in the coil equals ..........

1. A 100 Hz
2. B 75 Hz
3. C 50 Hz
4. D 25 Hz

An inductor has a self-inductance of $\frac{7}{44}$ H and an inductive reactance of 50 Ω. If its ohmic resistance is 30 Ω, then:
(2) the impedance of the coil equals ..........

1. A 80 Ω
2. B 58.31 Ω
3. C 50 Ω
4. D 18.75 Ω

The operating coil of a circuit regulator has an inductive reactance of 40 Ω and an ohmic resistance of 30 Ω, and it is connected to an AC source of voltage 5 V, so:
(1) the total impedance of the coil is ..........

1. A 70 Ω
2. B 60 Ω
3. C 50 Ω
4. D 10 Ω

The operating coil of a circuit regulator has an inductive reactance of 40 Ω and an ohmic resistance of 30 Ω, and it is connected to an AC source of voltage 5 V, so:
(2) the current through the coil is ..........

1. A 0.07 A
2. B 0.09 A
3. C 0.1 A
4. D 0.2 A

The operating coil of a circuit regulator has an inductive reactance of 40 Ω and an ohmic resistance of 30 Ω, and it is connected to an AC source of voltage 5 V, so:
(3) the phase angle between the total voltage and the current equals ..........

1. A 36.87°
2. B 51.34°
3. C 53.13°
4. D 59.03°

An electric lamp of resistance R is connected in different circuits with sources of negligible internal resistance. In which of the following circuits is the lamp brightest?

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

An AC source of emf 100 V and frequency 50 Hz works in a circuit containing an ohmic resistor of 30 Ω and an inductor of no resistance with a self-inductance of $\frac{7}{35}$ H, connected in series, so:
(1) the current equals ..........

1. A 1.44 A
2. B 1.37 A
3. C 1.07 A
4. D 0.5 A

An AC source of emf 100 V and frequency 50 Hz works in a circuit containing an ohmic resistor of 30 Ω and an inductor of no resistance with a self-inductance of $\frac{7}{35}$ H, connected in series, so:
(2) the phase angle between the total voltage and the current equals ..........

1. A 72.1°
2. B 64.49°
3. C 59.2°
4. D 51.42°

An AC source of emf 100 V and frequency 50 Hz works in a circuit containing an ohmic resistor of 30 Ω and an inductor of no resistance with a self-inductance of $\frac{7}{35}$ H, connected in series, so:
(3) the potential differences across the resistor and across the coil are, respectively, ..........

1. A 50 V, 50 V
2. B 20 V, 80 V
3. C 43.2 V, 56.8 V
4. D 43.2 V, 90.52 V

An ohmic resistor of 15 Ω is connected in series with an inductor of no ohmic resistance and an AC source of emf 60 V and negligible internal resistance. If the potential difference across the resistor is 45 V, then:
(1) the inductive reactance of the coil equals ..........

1. A 11.25 Ω
2. B 13.23 Ω
3. C 15 Ω
4. D 30 Ω

An ohmic resistor of 15 Ω is connected in series with an inductor of no ohmic resistance and an AC source of emf 60 V and negligible internal resistance. If the potential difference across the resistor is 45 V, then:
(2) the potential difference across the coil equals ..........

1. A 15 V
2. B 24.28 V
3. C 39.69 V
4. D 41.3 V

An AC circuit consists of an ohmic resistance X and an inductor of inductive reactance X connected in series. The phase angle between the total voltage and the current equals ..........

1. A 30°
2. B 45°
3. C 0°
4. D 90°

Two identical coils, each of self-inductance L and ohmic resistance R, are connected together with an AC source of voltage V, a switch K and an ohmic resistor R as in the opposite figure. When switch K is closed, the effective current and the phase angle between the total voltage and the current, respectively, ..........

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

An electric circuit consists of an AC source and an inductor of ohmic resistance R. The figure that represents the phase difference between the vectors of the potential difference (V) across the coil and the current (I) through it is ..........

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

Two identical inductors (x) and (y) are connected in an electric circuit as in figure (1). Figure (2) represents the phase difference between the vectors of the total voltage (V) and the current (I) in this circuit. Which of the following figures represents the phase difference between the total voltage (V) and the current (I) after switch (K) is opened?

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

An inductor of no resistance is connected in series with an AC source of emf 260 V and a hot-wire ammeter. The ammeter reads 2 A. If the ratio of the potential difference across the ammeter to the potential difference across the coil is $\frac{5}{12}$, then:
(1) the ratio of the ammeter resistance to the inductive reactance of the coil is ..........

1. A $\dfrac{5}{12}$
2. B $\dfrac{12}{5}$
3. C $\dfrac{1}{2}$
4. D $\dfrac{2}{1}$

An inductor of no resistance is connected in series with an AC source of emf 260 V and a hot-wire ammeter. The ammeter reads 2 A. If the ratio of the potential difference across the ammeter to the potential difference across the coil is $\frac{5}{12}$, then:
(2) the impedance of the circuit equals ..........

1. A 138 Ω
2. B 130 Ω
3. C 10 Ω
4. D 24 Ω

An inductor of no resistance is connected in series with an AC source of emf 260 V and a hot-wire ammeter. The ammeter reads 2 A. If the ratio of the potential difference across the ammeter to the potential difference across the coil is $\frac{5}{12}$, then:
(3) the resistance of the hot-wire ammeter equals ..........

1. A 130 Ω
2. B 120 Ω
3. C 100 Ω
4. D 50 Ω

An inductor of no resistance is connected in series with an AC source of emf 260 V and a hot-wire ammeter. The ammeter reads 2 A. If the ratio of the potential difference across the ammeter to the potential difference across the coil is $\frac{5}{12}$, then:
(4) the inductive reactance of the coil equals ..........

1. A 130 Ω
2. B 120 Ω
3. C 100 Ω
4. D 50 Ω

In the opposite circuit, the current in the circuit is 1 A and the potential difference between points a and b is 80 V. After switch $(K_1)$ is opened and switch $(K_2)$ is closed, the potential difference between a and b stays 80 V. The ohmic resistance (R) equals ..........

1. A 40 Ω
2. B 50 Ω
3. C 60 Ω
4. D 80 Ω

When a coil is connected to a DC source of emf 11 V, the current in it is 2.2 A. When the coil is connected to an AC source of frequency 50 Hz and emf 13 V, the current in the coil is 1 A. The self-inductance of the coil is ..........

1. A 0.01 H
2. B 0.025 H
3. C 0.03 H
4. D 0.038 H

An inductor of self-inductance $\frac{7}{275}$ H and ohmic resistance 6 Ω is connected to a source of emf 6 V and negligible internal resistance. The current in the coil, if the source voltage is:
(1) alternating with frequency 50 Hz, equals ..........

1. A 0.2 A
2. B 0.42 A
3. C 0.6 A
4. D 1 A

An inductor of self-inductance $\frac{7}{275}$ H and ohmic resistance 6 Ω is connected to a source of emf 6 V and negligible internal resistance. The current in the coil, if the source voltage is:
(2) direct, equals ..........

1. A 0
2. B 0.42 A
3. C 0.6 A
4. D 1 A

An inductor of self-inductance 0.1 H is connected to a DC source of emf 100 V as in circuit (1), and the electric power consumed in the coil is 100 W. It is connected a second time to an AC source of effective voltage 100 V and frequency 60 Hz as in circuit (2). Neglecting the internal resistance of the two sources, the electric power consumed in the coil ..........

1. A stays 100 W
2. B becomes 187.5 W
3. C becomes 87.5 W
4. D becomes 12.5 W

An inductor of self-inductance 2 H is connected in series with a resistance of 1950 Ω and an AC source of frequency $\frac{500}{\pi}$ Hz. The phase angle between the current and the total voltage is 45°, so the ohmic resistance of the coil equals ..........

1. A 500 Ω
2. B 250 Ω
3. C 150 Ω
4. D 50 Ω

In the opposite circuit, an AC source of voltage 200 V is connected to a lamp of resistance 100 Ω and an inductor of inductive reactance 60 Ω, and a current of 2 A passes in the circuit. The electric power consumed in the lamp after switch (K) is opened is approximately ..........

1. A 111 W
2. B 222 W
3. C 333 W
4. D 444 W

An AC circuit consists of an AC source of angular frequency (ω), an ohmic resistor (R) and an inductor of negligible ohmic resistance whose self-inductance can be changed. The opposite graph represents the relation between the square of the circuit impedance $(Z^2)$ and the square of the self-inductance of the coil $(L^2)$, so ..........

1. A ohmic resistance (R): $10^2$ Ω, angular frequency of the source (ω): 29.05 rad/s
2. B ohmic resistance (R): $10^2$ Ω, angular frequency of the source (ω): 182.6 rad/s
3. C ohmic resistance (R): $10^4$ Ω, angular frequency of the source (ω): 29.05 rad/s
4. D ohmic resistance (R): $10^4$ Ω, angular frequency of the source (ω): 182.6 rad/s

An AC circuit contains an AC source and two pure elements x and y connected in series. The opposite graph shows how each of the voltages $(V_x)$ and $(V_y)$ in volts and the current (I) in amperes change with time, so:
(1) the elements x and y are, respectively, ..........

1. A an ohmic resistor, an inductor
2. B an inductor, an ohmic resistor
3. C an ohmic resistor, a capacitor
4. D a capacitor, an inductor

An AC circuit contains an AC source and two pure elements x and y connected in series. The opposite graph shows how each of the voltages $(V_x)$ and $(V_y)$ in volts and the current (I) in amperes change with time, so:
(2) the phase angle between the total voltage and the current equals ..........

1. A 26.56°
2. B 33.69°
3. C 36.86°
4. D 53.13°

An AC circuit contains an AC source and two pure elements x and y connected in series. The opposite graph shows how each of the voltages $(V_x)$ and $(V_y)$ in volts and the current (I) in amperes change with time, so:
(3) the emf of the source equals ..........

1. A 6 V
2. B 7.07 V
3. C 8 V
4. D 14 V

An AC circuit contains an AC source and two pure elements x and y connected in series. The opposite graph shows how each of the voltages $(V_x)$ and $(V_y)$ in volts and the current (I) in amperes change with time, so:
(4) the impedance of the circuit equals ..........

1. A 1 Ω
2. B 2 Ω
3. C 2.5 Ω
4. D 3.5 Ω

The opposite figure shows an AC circuit containing a capacitor C and an ohmic resistor R. Which of the following choices is correct?

1. A The potential difference $V_2$ and the current I are in phase
2. B The potential difference $V_1$ leads the potential difference $V_2$ in phase
3. C The potential difference $V_1$ and the current I are in phase
4. D The potential differences $V_1$, $V_2$ and the current I are all in phase

The impedance of an AC circuit containing a capacitor and an ohmic resistor is ..........

1. A equal to the difference between the capacitive reactance and the resistance
2. B zero
3. C equal to the algebraic sum of the capacitive reactance and the resistance
4. D less than the algebraic sum of the capacitive reactance and the resistance

The current in an AC circuit with a variable capacitor and a rheostat connected in series increases when ..........

1. A the capacitance is increased
2. B the capacitance is decreased
3. C the rheostat resistance is increased
4. D the frequency of the AC source is decreased

A capacitor C and an ohmic resistor R are connected in series to an AC generator (dynamo), and the capacitive reactance equals the resistance R. If the rotation frequency of the dynamo coil decreases, the relation between the potential difference across the capacitor and the potential difference across the resistor becomes ..........

1. A $V_R > V_C$
2. B $V_C > V_R$
3. C $V_R = V_C = 0$
4. D $V_R = V_C \neq 0$

An AC source of frequency $\frac{50}{\pi}$ Hz is connected in a circuit containing an ohmic resistor of 1 kΩ and another component. The phase difference between the total voltage and the current in the circuit is $\frac{\pi}{4}$, so the other component in the circuit is ..........

1. A a capacitor of capacitance 10 μF
2. B a capacitor of capacitance 1 μF
3. C an inductor of self-inductance 5 H
4. D an inductor of self-inductance 1 H

In the opposite circuit, the capacitive reactance equals the ohmic resistance (R), and the instantaneous potential difference across the source is given by $V = 20 \sin \omega t$. The instantaneous current in the circuit is given by ..........

1. A $I = \dfrac{20}{R} \sin \left(\omega t + \dfrac{\pi}{4}\right)$
2. B $I = \dfrac{10\sqrt{2}}{R} \sin \left(\omega t + \dfrac{\pi}{6}\right)$
3. C $I = \dfrac{10\sqrt{2}}{R} \sin \left(\omega t - \dfrac{\pi}{4}\right)$
4. D $I = \dfrac{10\sqrt{2}}{R} \sin \left(\omega t + \dfrac{\pi}{4}\right)$

In the circuit shown in the figure, when the capacitance is $C_1$ the phase angle between the current and the total voltage is 30°. If the capacitance is changed to $C_2$, the phase angle becomes 60°, so ..........

1. A $C_2 = \dfrac{C_1}{3}$
2. B $C_2 = \dfrac{2 C_1}{3}$
3. C $C_2 = \dfrac{2 C_1}{5}$
4. D $C_2 = \dfrac{3 C_1}{5}$

In the AC circuit shown, if the potential difference across the capacitor C is 3 V, the potential difference across the resistor R equals ..........

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

In the circuit shown, if the effective current in the circuit is 2 A, R equals ..........

1. A 4 Ω
2. B 6 Ω
3. C 8 Ω
4. D 12 Ω

The opposite figure shows an AC circuit. When the potential difference across the capacitor equals the potential difference across the ohmic resistor, the source frequency equals ..........

1. A 50 Hz
2. B 60 Hz
3. C 100 Hz
4. D 500 Hz

A capacitor of capacitance $\frac{7}{22}$ μF is connected to a non-inductive ohmic resistor of 1000 Ω. If an alternating current of frequency 500 Hz passes through them, then:
(1) the total impedance is ..........

1. A 1414.2 Ω
2. B 2000 Ω
3. C 318.2 Ω
4. D $5 \times 10^4$ Ω

A capacitor of capacitance $\frac{7}{22}$ μF is connected to a non-inductive ohmic resistor of 1000 Ω. If an alternating current of frequency 500 Hz passes through them, then:
(2) the total voltage lags behind the current by a phase angle of ..........

1. A 50°
2. B 45°
3. C 90°
4. D 63.75°

In the opposite circuit, if the capacitive reactance $X_C$ is three times the ohmic resistance R, the impedance Z equals ..........

1. A $\sqrt{2}$ R
2. B R
3. C $\sqrt{10}$ R
4. D 4 R

In the circuit shown, when a current of frequency f passes, $(X_C = R)$. If the frequency increases to 2 f, the impedance ..........

1. A doubles
2. B is halved
3. C becomes 1.1 R
4. D becomes 0.5 R

The opposite figure shows the vectors of the current (I) and the total voltage (V) of an AC circuit containing two pure elements X and Y connected in series with an AC source. The elements X and Y could be ..........

1. A an ohmic resistor and a capacitor
2. B an ohmic resistor and a coil
3. C a coil and a capacitor
4. D an ohmic resistor and an ohmic resistor

An inductor of negligible ohmic resistance is connected with an unknown element (y) and an AC source as in the figure. It is found that the total potential difference = the potential difference across the coil + the potential difference across y. So the element (y) is ..........

1. A an ohmic resistor
2. B an inductor of negligible ohmic resistance
3. C a capacitor
4. D an inductor with ohmic resistance

The opposite figure represents the vectors of the total voltage (V) and the current (I) in a series AC circuit made of an AC source and two pure elements (a, b). The elements (a, b) are ..........

1. A an ohmic resistor and an inductor
2. B an ohmic resistor and a capacitor
3. C two ohmic resistors
4. D an inductor and a capacitor

An AC source, a hot-wire ammeter and an ohmic resistor are connected once with an inductor of negligible ohmic resistance as in circuit (1), and once with a capacitor as in circuit (2). If the hot-wire ammeter reading is the same in both circuits, which of the following statements is NOT correct?

1. A The inductive reactance of the coil = the capacitive reactance of the capacitor
2. B The voltage across the coil = the voltage across the capacitor
3. C The current lags behind the total voltage by an angle θ in both circuits
4. D The impedances of the two circuits are equal

An AC source of frequency 50 Hz is connected with an inductor of self-inductance $\frac{1}{\pi}$ H and negligible ohmic resistance, a capacitor of capacitance $\frac{100}{\pi}$ μF and a lamp, as in the opposite circuit. What happens to the brightness of the lamp after switch $(K_1)$ is opened and switch $(K_2)$ is closed?

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

A resistance of 300 Ω is connected in series with a capacitor of reactance 265 Ω and an AC source of frequency 100 Hz. If the potential difference across the capacitor = 5 V, then:
(1) the capacitance equals ..........

1. A 0.42 μF
2. B 0.9 μF
3. C 3 μF
4. D 6 μF

A resistance of 300 Ω is connected in series with a capacitor of reactance 265 Ω and an AC source of frequency 100 Hz. If the potential difference across the capacitor = 5 V, then:
(2) the current in the circuit is approximately ..........

1. A 0.008 A
2. B 0.017 A
3. C 0.019 A
4. D 0.01 A

A resistance of 300 Ω is connected in series with a capacitor of reactance 265 Ω and an AC source of frequency 100 Hz. If the potential difference across the capacitor = 5 V, then:
(3) the potential difference across the resistor equals ..........

1. A 4.7 V
2. B 5 V
3. C 5.7 V
4. D 6 V

An AC source of emf 200 volts and frequency 50 hertz is connected in series with a capacitor of capacitance $\frac{100}{3\pi}$ microfarad and a lamp marked (25 watt, 100 volt). The current through the lamp filament is ..........

1. A 0.15 A, so it does not light
2. B 0.2 A, so it lights
3. C 0.4 A, so it melts
4. D 0.45 A, so it melts

In the circuit shown, the phase angle between the current and the total voltage is 45°. The phase angle between them when:
(1) the capacitor is connected in series with another capacitor of capacitance C becomes ..........

1. A 26.57°
2. B −63.4°
3. C 63.4°
4. D −26.57°

In the circuit shown, the phase angle between the current and the total voltage is 45°. The phase angle between them when:
(2) the resistor is connected in series with another resistor R becomes ..........

1. A 26.57°
2. B −63.4°
3. C −26.57°
4. D 63.4°

In the circuit shown, if the effective current in the circuit is 0.02 A, the resistance R is ..........

1. A 11590.91 Ω
2. B 10000 Ω
3. C 9872.64 Ω
4. D 8409.81 Ω

In the circuit shown, the capacitance at which:
(1) the effective current is 0.25 A is ..........

1. A 1.53 μF
2. B 2.65 μF
3. C 3.42 μF
4. D 4.59 μF

In the circuit shown, the capacitance at which:
(2) the phase angle between the current and the total voltage is (−45°) equals ..........

1. A 5.3 μF
2. B 4.33 μF
3. C 2.65 μF
4. D 1.42 μF

In the circuit shown, the total ohmic resistance is 500 Ω and the hot-wire ammeter reads 0.2 A when switch K is open. Its reading when switch K is closed is ..........

1. A 0.4 A
2. B 0.3 A
3. C 0.27 A
4. D 0.2 A

In the following circuits, all the sources are identical, each capacitor has capacitance (C) and each lamp has resistance (R). In which of these circuits is the lamp brightest?

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

An AC circuit contains an inductor L of no resistance and a capacitor C connected in series. The potential difference $V_L$ ..........

1. A leads $V_C$ in phase by 90°
2. B lags behind $V_C$ in phase by 90°
3. C is in phase with $V_C$
4. D leads $V_C$ in phase by 180°

An LC AC circuit consists of a source whose frequency can be changed, a capacitor and an inductor of negligible ohmic resistance connected in series. When the source frequency is (f), the capacitive reactance $(X_C)$ is 500 Ω and the inductive reactance $(X_L)$ is 100 Ω. The change in the phase angle between the total voltage and the current after:
(1) the source frequency is increased to (2 f) equals ..........

1. A 0°
2. B 45°
3. C 90°
4. D 180°

An LC AC circuit consists of a source whose frequency can be changed, a capacitor and an inductor of negligible ohmic resistance connected in series. When the source frequency is (f), the capacitive reactance $(X_C)$ is 500 Ω and the inductive reactance $(X_L)$ is 100 Ω. The change in the phase angle between the total voltage and the current after:
(2) the source frequency is increased to (5 f) equals ..........

1. A 0°
2. B 45°
3. C 90°
4. D 180°

In a series AC circuit, it is found that the current at some instant is zero when the potential difference across the source is maximum. The AC source could be connected with ..........

1. A an inductor of no ohmic resistance
2. B a capacitor
3. C an inductor of no resistance and a capacitor
4. D all of the above

The current in the opposite circuit equals ..........

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

In the circuit shown, if $V_1 = V$, then $V_2$ equals ..........

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

In the circuit shown, an AC source is connected in series with a variable capacitor of capacitive reactance $(X_C)_1$ and an inductor of no ohmic resistance with inductive reactance $X_L$, where $X_L > (X_C)_1$, and the effective current is I. If the capacitance is reduced to a quarter, $(X_C)_2$ becomes greater than $X_L$ and the effective current doubles. The ratio $\frac{X_L}{(X_C)_1}$ is ..........

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

An AC source of frequency f is connected in series with a capacitor and an inductor of no ohmic resistance. The capacitive reactance is twice the inductive reactance. If the source frequency is doubled, the capacitive reactance becomes .......... the inductive reactance.

1. A twice
2. B equal to
3. C half
4. D four times

When the source in the circuit shown is replaced by another source of the same voltage and a higher frequency, which of the following choices is correct?

1. A Reading of hot-wire ammeter $A_1$: increases, reading of hot-wire ammeter $A_2$: decreases
2. B Reading of hot-wire ammeter $A_1$: decreases, reading of hot-wire ammeter $A_2$: increases
3. C Reading of hot-wire ammeter $A_1$: decreases, reading of hot-wire ammeter $A_2$: decreases
4. D Reading of hot-wire ammeter $A_1$: increases, reading of hot-wire ammeter $A_2$: increases

In which of the elements shown in the opposite circuit is electrical energy converted into heat energy?

1. A The ohmic resistor (R)
2. B The inductor (L)
3. C The capacitor (C)
4. D All three elements

The opposite figure shows a phasor diagram of the potential difference and the current in an AC circuit. This circuit could be ..........

1. A RLC only
2. B RL only
3. C RC only
4. D RL or RLC

In the opposite circuit, the capacitance was adjusted until $(X_C)_1 = \frac{1}{2} X_L$, and the current in the circuit was I. If the capacitance is decreased gradually until $(X_C)_2 = \frac{3}{2} X_L$, the current in the circuit ..........

1. A decreases until it becomes zero
2. B decreases until it becomes zero, then increases
3. C increases
4. D increases then decreases until it reaches the same first value

The opposite figure shows the voltage vectors in an RLC circuit. The total impedance of the circuit equals ..........

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

In the opposite circuit, the voltage of the AC source is ..........

1. A 40 V
2. B 50 V
3. C 70 V
4. D 110 V

When a capacitor is added in series to the circuit shown, the reading of the hot-wire ammeter does not change. In this case the capacitive reactance of the capacitor is .......... the inductive reactance of the coil.

1. A half
2. B equal to
3. C twice
4. D three times

An AC circuit consists of a resistor R, an inductor L of negligible ohmic resistance and a capacitor C connected in series, where $X_C = 2 X_L = 2 R$. The total potential difference ..........

1. A leads $V_R$ in phase by 90°
2. B leads $V_R$ in phase by 45°
3. C lags behind $V_R$ in phase by 90°
4. D lags behind $V_R$ in phase by 45°

A series RLC AC circuit has a total impedance of 20 Ω, an ohmic resistance of 10 Ω, and the inductive reactance of the coil is greater than the capacitive reactance of the capacitor. So the phase angle between the total voltage and the current equals ..........

1. A 30°
2. B 45°
3. C 60°
4. D 90°

In the AC circuit shown:
(1) the total impedance is ..........

1. A 1000 Ω
2. B 2000 Ω
3. C 5000 Ω
4. D $1000\sqrt{2}$ Ω

In the AC circuit shown:
(2) the phase angle between the total voltage and the current is ..........

1. A 90°
2. B 30°
3. C 45°
4. D 0°

If the phase angle between the total voltage and the current in an RLC circuit is 45° and $(R = X_C)$, the ratio of the inductive reactance of the coil to the capacitive reactance of the capacitor $\left(\frac{X_L}{X_C}\right)$ equals ..........

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

An AC circuit contains a source of frequency $\frac{500}{\pi}$ Hz and effective voltage 200 V, an inductor of self-inductance 0.08 H and ohmic resistance 30 Ω, and a capacitor, all connected in series. If the total impedance of the circuit is 50 Ω, the phase angle between the total voltage and the current equals ..........

1. A 42.19°
2. B 46.12°
3. C 49.17°
4. D 53.13°

An AC source of effective voltage 50 V and frequency $\frac{500}{\pi}$ Hz is connected in series with an ohmic resistor of 300 Ω, a coil of negligible ohmic resistance and self-inductance 0.9 H, and a capacitor of capacitance 2 μF, so:
(1) the impedance of the circuit equals ..........

1. A 500 Ω
2. B 806.23 Ω
3. C 1431.78 Ω
4. D 1700 Ω

An AC source of effective voltage 50 V and frequency $\frac{500}{\pi}$ Hz is connected in series with an ohmic resistor of 300 Ω, a coil of negligible ohmic resistance and self-inductance 0.9 H, and a capacitor of capacitance 2 μF, so:
(2) the current in the circuit equals ..........

1. A 0.03 A
2. B 0.1 A
3. C 0.17 A
4. D 0.25 A

An AC source of effective voltage 50 V and frequency $\frac{500}{\pi}$ Hz is connected in series with an ohmic resistor of 300 Ω, a coil of negligible ohmic resistance and self-inductance 0.9 H, and a capacitor of capacitance 2 μF, so:
(3) the power consumed in the circuit equals ..........

1. A 4 W
2. B 3 W
3. C 2 W
4. D 1.47 W

A circuit consists of a resistance of 15 Ω, a coil of self-inductance 0.08 H and a capacitor of capacitance 30 μF, all connected in series with an AC generator (dynamo) whose coil has an angular velocity of 500 rad/s. The total voltage ..........

1. A leads the current by 81.9°
2. B lags behind the current by 60.65°
3. C leads the current by 60.65°
4. D lags behind the current by 81.9°

An inductor of negligible ohmic resistance, an ohmic resistor and a capacitor are connected in series with an AC source as in the opposite figure. The voltmeter readings are related by $V_2 = V_3 = 2 V_1$. When a soft iron rod is put inside the coil, the readings of voltmeters $V_1$ and $V_2$, respectively, ..........

1. A decrease, decrease
2. B decrease, increase
3. C increase, decrease
4. D increase, increase

Which of the following choices represents the components that can be placed at position X so that the phase angle between the total voltage and the current becomes 45°? (The ohmic resistance of the coils is negligible.)

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

An electric circuit consists of a capacitor of capacitive reactance 80 Ω, an inductor of self-inductance 0.28 H, and an ohmic resistor that is a wire 12 m long with a cross-sectional area of $7 \times 10^{-5}$ m² and a resistivity of $35 \times 10^{-6}$ Ω.m, all connected in series with an AC source of negligible internal resistance, frequency 50 Hz and effective emf 20 V, so:
(1) the maximum current in the circuit is ..........

1. A 2 A
2. B 2.828 A
3. C 3 A
4. D 3.828 A

An electric circuit consists of a capacitor of capacitive reactance 80 Ω, an inductor of self-inductance 0.28 H, and an ohmic resistor that is a wire 12 m long with a cross-sectional area of $7 \times 10^{-5}$ m² and a resistivity of $35 \times 10^{-6}$ Ω.m, all connected in series with an AC source of negligible internal resistance, frequency 50 Hz and effective emf 20 V, so:
(2) the effective potential differences across the capacitor and across the coil, respectively, are approximately ..........

1. A 248.86 V, 226.24 V
2. B 176 V, 160 V
3. C 160 V, 176 V
4. D 226.24 V, 248.86 V

A coil of self-inductance $\frac{7}{220}$ henry and ohmic resistance 4 ohm is connected in series with a capacitor of capacitive reactance 5 ohm and a variable ohmic resistor (R). The ends of the group are connected to an AC source of emf 13 volt, frequency 50 hertz and negligible internal resistance. If the effective current in the coil must not exceed one ampere, the least ohmic resistance (R) that must be used to keep the circuit safe equals ..........

1. A 4 Ω
2. B 8 Ω
3. C 10 Ω
4. D 12 Ω

From the circuit shown:
(1) the total impedance of the circuit is ..........

1. A 5 Ω
2. B 7 Ω
3. C 24 Ω
4. D 39 Ω

From the circuit shown:
(2) the current in the circuit equals ..........

1. A 0.51 A
2. B 1 A
3. C 2.85 A
4. D 4 A

From the circuit shown:
(3) the readings of the four voltmeters $V_1$, $V_2$, $V_3$, $V_4$ are ..........

1. A $V_1$: 80 V, $V_2$: 12 V, $V_3$: 16 V, $V_4$: 20 V
2. B $V_1$: 12 V, $V_2$: 20 V, $V_3$: 20 V, $V_4$: 0 V
3. C $V_1$: 12 V, $V_2$: 80 V, $V_3$: 64 V, $V_4$: 16 V
4. D $V_1$: 64 V, $V_2$: 16 V, $V_3$: 12 V, $V_4$: 144 V

In the opposite circuit, the current in the circuit is 1 A, the inductive reactance of the coil is 180 Ω and each voltmeter reads 100 V, so:
(1) the capacitive reactance of the capacitor equals ..........

1. A 60 Ω
2. B 80 Ω
3. C 180 Ω
4. D 280 Ω

In the opposite circuit, the current in the circuit is 1 A, the inductive reactance of the coil is 180 Ω and each voltmeter reads 100 V, so:
(2) the resistance (R) equals ..........

1. A 60 Ω
2. B 80 Ω
3. C 180 Ω
4. D 280 Ω

In the opposite circuit, the current in the circuit is 1 A, the inductive reactance of the coil is 180 Ω and each voltmeter reads 100 V, so:
(3) the phase angle between the total voltage and the current in the circuit equals ..........

1. A 0°
2. B 29°
3. C 51°
4. D 59°

In the circuit shown, the phase angle between the total voltage and the current is 30°. When the capacitor is connected in parallel with another identical capacitor, the phase angle between the total voltage and the current becomes ..........

1. A 22.65°
2. B 36.24°
3. C 40.89°
4. D 50.92°

An AC circuit contains a coil of self-inductance 0.2 H and ohmic resistance 500 Ω, a variable capacitor and an AC source of voltage 400 V and frequency $\frac{5000}{\pi}$ Hz, all connected in series. The capacitance that makes the total voltage lag behind the current by $\frac{\pi}{4}$ equals ..........

1. A $5 \times 10^{-8}$ F
2. B $4 \times 10^{-8}$ F
3. C $6 \times 10^{-6}$ F
4. D $4 \times 10^{-6}$ F

Figure (1) shows an RLC AC circuit, and figure (2) shows graphically how the total voltage (V) of the circuit and the current (I) in it change with time (t). The capacitive reactance $(X_C)$ of the capacitor equals ..........

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

In the opposite circuit, when only the capacitor is removed, the total voltage leads the current in phase by 30°, and when only the coil is removed, the total voltage lags behind the current in phase by 60°. The current in the circuit shown in the figure is approximately ..........

1. A 3.78 A
2. B 7.56 A
3. C 9.45 A
4. D 18.92 A

In the opposite circuit, if the ratio of the readings of the two voltmeters $\left(\frac{V_1}{V_2}\right)$ is $\frac{1}{2}$, the capacitance (C) is approximately ..........

1. A 60 μF
2. B 30 μF
3. C 15 μF
4. D 7.5 μF

In the circuit shown, if the total voltage lags behind the current by 45°, the element A is ..........

1. A an inductor of inductive reactance 20 Ω
2. B an inductor of inductive reactance 80 Ω
3. C a capacitor of capacitive reactance 20 Ω
4. D a capacitor of capacitive reactance 60 Ω

An electric generator whose coil has negligible resistance consists of 500 turns, each of area $\frac{7}{11}$ m², placed in a uniform magnetic field of flux density $5 \times 10^{-4}$ T and rotating at a frequency of 50 Hz. Its ends are connected in series with a capacitor of capacitive reactance 110 Ω, an ohmic resistor of 40 Ω and an inductor of inductive reactance 80 Ω and negligible ohmic resistance, so:
(1) the maximum voltage across the inductor equals ..........

1. A 40 V
2. B $40\sqrt{2}$ V
3. C 80 V
4. D 110 V

An electric generator whose coil has negligible resistance consists of 500 turns, each of area $\frac{7}{11}$ m², placed in a uniform magnetic field of flux density $5 \times 10^{-4}$ T and rotating at a frequency of 50 Hz. Its ends are connected in series with a capacitor of capacitive reactance 110 Ω, an ohmic resistor of 40 Ω and an inductor of inductive reactance 80 Ω and negligible ohmic resistance, so:
(2) the effective value of the alternating current in the circuit equals ..........

1. A 0.707 A
2. B 1 A
3. C 1.41 A
4. D 2 A

In the opposite circuit, $X_C = 2 X_L = 2 R$ and the total voltage lags behind the source current by 45°. Which switches are closed so that the phase angle between the total voltage and the source current becomes zero?

1. A Switch $K_1$ only
2. B Switch $K_2$ only
3. C Switch $K_3$ only
4. D All three switches

The opposite figure shows a circuit containing an AC source of emf 220 V, a capacitor of capacitive reactance 800 Ω, a coil of inductive reactance 800 Ω, an electric lamp of resistance 600 Ω and a switch, all connected in series. The current:
(1) in the circuit equals ..........

1. A $\dfrac{1}{10}$ A
2. B $\dfrac{4}{10}$ A
3. C $\dfrac{11}{40}$ A
4. D $\dfrac{11}{30}$ A

The opposite figure shows a circuit containing an AC source of emf 220 V, a capacitor of capacitive reactance 800 Ω, a coil of inductive reactance 800 Ω, an electric lamp of resistance 600 Ω and a switch, all connected in series. The current:
(2) when only the capacitor is removed from the circuit equals ..........

1. A 0.16 A
2. B 0.22 A
3. C 0.36 A
4. D 0.4 A

The opposite figure shows a circuit containing an AC source of emf 220 V, a capacitor of capacitive reactance 800 Ω, a coil of inductive reactance 800 Ω, an electric lamp of resistance 600 Ω and a switch, all connected in series. The current:
(3) when only the coil is removed from the circuit equals ..........

1. A 0.4 A
2. B 0.36 A
3. C 0.22 A
4. D 0.16 A

The opposite figure shows a circuit containing an AC source of emf 220 V, a capacitor of capacitive reactance 800 Ω, a coil of inductive reactance 800 Ω, an electric lamp of resistance 600 Ω and a switch, all connected in series. The current:
(4) when both the capacitor and the coil are removed from the circuit equals ..........

1. A $\dfrac{11}{30}$ A
2. B $\dfrac{11}{40}$ A
3. C $\dfrac{4}{10}$ A
4. D $\dfrac{3}{10}$ A

An ohmic resistor R is connected in series with an inductor of self-inductance L and ohmic resistance R and an AC source. The potential differences across the coil and across the ohmic resistor are as shown in the opposite figure. Find:
(1) the ratio of the inductive reactance of the coil to its ohmic resistance.
(2) the potential difference between the source terminals.

Two identical resistance wires (x, y): wire x is wound double (non-inductively) as a solenoid, and wire y is wound singly as an inductor. The two coils are connected in series to an AC source. Explain why the potential difference across each coil is different from the other.

In the opposite circuit, the two coils are identical and have negligible ohmic resistance. What happens, with explanation, to the brightness of the lamp and to the phase angle between the total voltage and the current in the circuit when switch K is closed?

In the AC circuit shown in the opposite figure, the readings of the two voltmeters V₁ and V₂ are 30 V and 50 V respectively. If the two coils have negligible ohmic resistance, find:
(1) the potential difference between points x and y
(2) the potential difference between points z and m

In the opposite circuit, what happens to the voltmeter reading if the turns of the coil are moved apart from each other uniformly?

In the circuit shown, what happens to the current in the circuit when an ohmic resistor of 200 Ω is put in place of the inductor?

In the circuit shown in the figure, a lamp of resistance R and an inductor of inductive reactance $X_L = R$ and negligible ohmic resistance are connected to an AC source. Show what happens to the brightness of the lamp when:
(1) the source frequency is doubled while its emf stays constant.
(2) both the source frequency and its emf are doubled.

In the circuit shown in the figure, the capacitive reactance of capacitor C equals the ohmic resistance of wire a. If the wire is stretched uniformly until its length doubles, calculate the change in the phase angle between the total voltage and the current in the circuit.

The opposite figure shows an AC circuit consisting of a capacitor, a glowing lamp and an AC source whose effective voltage is constant and whose frequency can be changed. Explain why the lamp filament glows less when the source frequency decreases.

In the circuit shown in the figure, the phase angle between the current and the total voltage is $-30^\circ$. Show how the capacitance can be changed so that the phase angle becomes $-60^\circ$

In the opposite circuit, if the maximum charge collected on the capacitor plates is $300\sqrt{2}\ \mu C$, calculate the power consumed in the lamp.

In the opposite circuit, how can you, by removing only one component from the circuit:
(1) increase the phase angle between the total voltage and the current to the largest possible value?
(2) increase the current to the largest possible value?

An AC source of negligible internal resistance and two pure elements x and y are connected together in series. The opposite graph shows how the current and the potential difference across each element change with time:
(1) Identify the types of the two elements x and y
(2) Find the phase angle between the total voltage and the current in the circuit.

An AC circuit consists of an ohmic resistor of 50 Ω, a pure element (x) and an AC source of voltage 200 V as in figure (1), and the phase angle between the total voltage and the current is ($-45^\circ$). When element (x) is replaced by another pure element (y) as in figure (2), the phase angle becomes ($30^\circ$). If elements (x) and (y) are connected together in series with the source as in figure (3), what is the current in the circuit in figure (3)?

In the circuit shown in the opposite figure, what happens to the current in the circuit when switch K is closed?

An AC source with a constant effective voltage and a variable frequency is connected to two identical lamps, an inductor of negligible ohmic resistance and a capacitor as in the opposite figure. Given that the inductive reactance of the coil equals the capacitive reactance of the capacitor, explain why, when the source frequency is increased, lamp (2) becomes brighter than lamp (1).

The opposite circuit is an RLC circuit connected to an AC source:
(1) Calculate the potential difference across the capacitor plates ($V_C$).
(2) Explain why the potential difference across the capacitor plates ($V_C$) can be greater than the source voltage (V).

The opposite figure shows an RLC AC circuit. Calculate the electric power consumed in the circuit.

A circuit consists of a capacitor of capacitive reactance 30 Ω, an ohmic resistor of 44 Ω and a coil of inductive reactance 90 Ω and ohmic resistance 36 Ω, connected in series with an AC source of frequency 60 Hz and voltage 200 V. Calculate:
(1) the current in the circuit.
(2) the potential difference across the coil.

In the circuit shown, if $X_L = 2X_C$, what happens to the brightness of the lamp when:
(1) L is doubled?
(2) C is doubled?

In the circuit shown in the figure, ($X_C < X_L$). Explain why the phase angle between the total voltage (V) and the current (I) in the circuit increases after the capacitor is removed.

In the circuit shown in the figure, if the two coils have negligible ohmic resistance, what is the phase angle between the total voltage and the current in the circuit when switch K is:
(1) open?
(2) closed?

In the opposite AC circuit, when switch K is closed, the phase angle between the total voltage and the current .......... (Trial exam / May 2021)

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

The opposite figure shows an AC circuit consisting of an AC source of maximum voltage 250 V, an inductor of negligible ohmic resistance and a hot-wire ammeter of ohmic resistance 12 Ω, connected in series. If the ammeter reads 10 A, the inductive reactance of the coil equals .......... (Trial exam / May 2021)

1. A 17.67 Ω
2. B 12.98 Ω
3. C 21.93 Ω
4. D 5.68 Ω

In the circuit shown, when switch (K) is closed, the phase angle between the total voltage (V) and the current (I) .......... (Trial exam / June 2021)

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

In the circuit shown, when the source is replaced by another of lower frequency with (V) constant, .......... (1st session 2021)

1. A inductive reactance of the coil: decreases, phase angle between the total voltage and the current: increases
2. B inductive reactance of the coil: increases, phase angle between the total voltage and the current: decreases
3. C inductive reactance of the coil: decreases, phase angle between the total voltage and the current: decreases
4. D inductive reactance of the coil: increases, phase angle between the total voltage and the current: increases

In the circuit shown, when switch (K) is closed, the phase angle between the total voltage (V) and the current (I) .......... (2nd session 2021, Sample exam 2025)

1. A decreases
2. B stays constant
3. C increases
4. D becomes zero

The figure shows a circuit with an ohmic resistor and an inductor (L) of negligible ohmic resistance, and the phase angle between the total voltage and the current is (θ). When switch (K) is closed, the phase angle between the voltage and the current .......... (1st session 2022)

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

The figure shows an AC circuit with an ohmic resistor and two inductors of negligible ohmic resistance. When switch (K) was open, the phase angle between the total voltage and the current was (θ). If switch (K) is closed, the phase angle between the total voltage and the current .......... (2nd session 2022)

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

In the opposite circuit, an inductor (of negligible ohmic resistance) has its turns spread uniformly. When $\frac{1}{4}$ of the length of the coil is cut off and the rest is connected in the circuit without changing the other factors, the phase angle between the total voltage and the current decreases by .......... (1st session 2023)

1. A $8.13^\circ$
2. B $36.87^\circ$
3. C $30.96^\circ$
4. D $14.04^\circ$

A straight wire is connected to an AC source and the effective current in it is I. Then the wire is wound as an inductor and connected to the same source. The effective current in it .......... (Sample exam 2025)

1. A decreases
2. B stays constant
3. C increases
4. D the answer cannot be determined

In an AC circuit, an inductor of inductive reactance 40 Ω and ohmic resistance 30 Ω is connected to an AC source of effective voltage 60 V. The electric power consumed in the circuit equals .......... (Sample exam 2025)

1. A 43.2 W
2. B 51.4 W
3. C 72 W
4. D 120 W

An inductor of no ohmic resistance is connected in series with an electric lamp of ohmic resistance R and a battery of emf V and negligible internal resistance. The current in the circuit is I and the power consumed in the lamp is $P_w$. When an AC source of effective voltage V is connected instead of the battery, the current in the circuit is 0.75 I. The power consumed in the lamp and the phase angle between the total voltage and the current in this case are, respectively, .......... (Sample exam 2025)

1. A $\frac{9P_w}{16}$ , $41.41^\circ$
2. B $\frac{9P_w}{16}$ , $36.89^\circ$
3. C $\frac{3P_w}{4}$ , $48.6^\circ$
4. D $\frac{3P_w}{4}$ , $41.41^\circ$

The figure shows an ideal transformer. When the AC source is replaced by a battery whose emf equals the effective voltage of the AC source, the brightness of lamps A and B, respectively, .......... (Sample exam 2025)

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

In the circuit shown, the phase angle between the total potential difference $V_t$ and the current I = .......... (1st session 2022)

1. A $38^\circ$
2. B $35^\circ$
3. C $-38^\circ$
4. D $-35^\circ$

A circuit contains a hot-wire ammeter of resistance 50 Ω, a capacitor and an AC source as in the figure. The maximum emf of the source equals .......... (2nd session 2021)

1. A 250.19 V
2. B 353.84 V
3. C 194.17 V
4. D 318.62 V

An AC source producing a maximum emf of $100\sqrt{2}$ V is connected to three capacitors and a hot-wire ammeter as in the figure. Using the data shown, the capacitive reactance $(X_C)_3$ equals .......... (2nd session 2022)

1. A 80 Ω
2. B 20 Ω
3. C 40 Ω
4. D 50 Ω

In the circuit shown, the phase angle between the total voltage and the current was ($-45^\circ$). When switch K is closed, the angle becomes .......... (Sample exam 2025)

1. A $0^\circ$
2. B $-26.6^\circ$
3. C $-63.4^\circ$
4. D $-90^\circ$

An AC source of frequency $\frac{100}{\pi}$ Hz and effective voltage 20 V is connected in series with an ohmic resistor of 3 Ω and a capacitor of capacitance 1250 µF. The charge collected on one plate of the capacitor when it is fully charged is .......... (Sample exam 2025)

1. A 0.020 C
2. B 0.025 C
3. C 0.028 C
4. D 0.035 C

The opposite figure shows an RLC circuit connected to an AC source of emf 200 V and frequency 50 Hz. The total impedance of the circuit is approximately .......... (Trial exam / May 2021)

1. A 40 Ω
2. B 50 Ω
3. C 100 Ω
4. D 30 Ω

The opposite figure shows an AC circuit with a capacitor, an inductor of negligible ohmic resistance, two resistors R₁ and R₂ and three switches K₁, K₂ and K₃. The largest electric power consumed is obtained when .......... (1st session 2024)

1. A switches K₁, K₂ and K₃ are open
2. B switch K₂ is open and switches K₁ and K₃ are closed
3. C switches K₂ and K₃ are closed and switch K₁ is open
4. D switches K₁, K₂ and K₃ are closed

In the circuit shown in the figure, if the coil is replaced by another one of the same length, the same cross-sectional area and the same wire material, but with twice the number of turns of the original coil, the ratio of (the circuit impedance in the second case) to (the circuit impedance in the first case) = .......... (1st session 2024)

1. A $\sqrt{10}$
2. B $20\sqrt{10}$
3. C $\frac{1}{\sqrt{10}}$
4. D $\frac{1}{20\sqrt{2}}$

From the data shown on the two circuits (1) and (2), the ratio ($\frac{Z_1}{Z_2}$) = .......... (2nd session 2024)

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

In a series (RLC) AC circuit, the phase angle between the potential difference across the coil ($V_L$) and the potential difference across the capacitor ($V_C$) is .......... (Sample exam 2025)

1. A $180^\circ$
2. B $90^\circ$
3. C $-90^\circ$
4. D $0^\circ$

In the circuit shown in the figure, an AC source of 220 V, 50 Hz is connected in series with a capacitor, an ohmic resistor and an inductor of negligible ohmic resistance. What are the total impedance of the circuit and the phase angle between the total voltage and the current? (Given: π = 3.14) (2nd session 2025)

1. A impedance: 24 Ω, phase angle: $0^\circ$
2. B impedance: 21.22 Ω, phase angle: $74.21^\circ$
3. C impedance: 48 Ω, phase angle: $60^\circ$
4. D impedance: 48 Ω, phase angle: $30.2^\circ$

The figure shows an electric circuit. Explain what happens to the phase angle between the total voltage and the current after switch (K) is closed. (Trial exam 2023)