Electric Current and Ohm's Law questions

In which of the following electric circuits does the direction of the arrows correctly show the conventional direction of the current?

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

The opposite figure shows part of an electric circuit carrying a direct current (I). Which of the two ammeters in the figure has the greater reading?

1. A Ammeter A₁
2. B Ammeter A₂
3. C Both ammeters have the same reading
4. D The answer cannot be determined

If the electric current in a conductor is 2 A, then:
the quantity of charge passing through a cross-section of the conductor in 10 s is ..........

1. A 0.2 C
2. B 8 C
3. C 12 C
4. D 20 C

If the electric current in a conductor is 2 A, then:
the time needed for a charge of 4 mC to pass through a cross-section of the conductor is ..........

1. A 2 ms
2. B 4 ms
3. C 6 ms
4. D 8 ms

In the opposite figure, a negative charge of 2 μC passes through cross-section x of a conductor in 4 ms. The magnitude and direction of the conventional current are ..........

1. A 8 mA, from x to y
2. B 8 mA, from y to x
3. C 0.5 mA, from x to y
4. D 0.5 mA, from y to x

If the rate of flow of free electrons through a cross-section of wire x is $10^{20}$ electron/s and through a cross-section of wire y is $2 \times 10^{20}$ electron/s, then the ratio between the currents in the two wires $\left(\frac{I_x}{I_y}\right)$ equals ..........

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

The opposite graph shows the relation between the quantity of charge (Q) passing through a cross-section of a conductor in a DC circuit and time (t). The direct current is ..........

1. A 2 A
2. B 10 A
3. C 50 A
4. D 250 A

The opposite graph shows the relation between the charge (Q) passing through cross-sections of two conductors x, y and time (t). The ratio between the currents in the two conductors $\left(\frac{I_x}{I_y}\right)$ is ..........

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

The opposite graph shows the relation between the number of electrons (N) passing through a certain cross-section of a conductor in a circuit carrying a current and time (t). The graph that represents the relation between the current (I) in this conductor and time (t) is ..........

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

The opposite graph shows the relation between the current (I) in a conductor and the time of its flow (t). The quantity of charge passing through a cross-section of the conductor in 10 s equals ..........

1. A 5 C
2. B 10 C
3. C 15 C
4. D 50 C

The opposite figure shows a charge of 2 μC revolving with a frequency of 1000 Hz in a uniform circular path. The current produced by the revolving charge equals ..........

1. A 5 mA
2. B 2 mA
3. C 500 A
4. D 2000 A

In the two opposite figures, two particles x, y carrying charges Q, 2Q respectively revolve in two circular paths. The ratio between the currents produced by the revolving particles $\left(\frac{I_x}{I_y}\right)$, if they revolve:
with the same frequency, equals ..........

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

In the two opposite figures, two particles x, y carrying charges Q, 2Q respectively revolve in two circular paths. The ratio between the currents produced by the revolving particles $\left(\frac{I_x}{I_y}\right)$, if they revolve:
with the same linear speed, equals ..........

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

According to Bohr's model of the hydrogen atom, the electron moves in a circular path of radius 0.53 Å with a speed of $2.2 \times 10^{6}$ m/s. The electric current produced by the motion of the electron equals ..........

1. A 3.141 mA
2. B 6.282 mA
3. C 1.166 mA
4. D 1.057 mA

In an electric circuit, the battery is a source of ..........

1. A positive charges
2. B negative charges
3. C electrical conductivity
4. D electrical energy

The ends of a metal conductor are connected to a DC source to form a closed circuit. Which of the following statements is correct about the motion of the free electrons inside and outside the source?

1. A They vibrate in their places without moving to new places
2. B Inside the source they move towards the terminal of higher potential
3. C Outside the source they move towards the terminal of lower potential
4. D Outside the source they move towards the terminal of higher potential

In which of the following cases does the arrow show the direction of motion of the free electrons through the resistor between points a, b?

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

In the opposite figure, the work done to move a charge of 4 C between points x, y is ..........

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

The potential difference between two points when a work of 30 J is needed to move a charge of 10 C between them equals ..........

1. A 0.3 V
2. B 3 V
3. C 30 V
4. D 300 V

If the work done to move a charge of 5 C between two points in a conductor is 100 J, and this charge passes through a cross-section of the conductor in 1 s, then:
the potential difference between the two points equals ..........

1. A 0.05 V
2. B 5 V
3. C 10 V
4. D 20 V

If the work done to move a charge of 5 C between two points in a conductor is 100 J, and this charge passes through a cross-section of the conductor in 1 s, then:
the current in the conductor equals ..........

1. A 2.5 A
2. B 5 A
3. C 7 A
4. D 12 A

If the work done to move a charge of 5 C between two points in a conductor is 100 J, and this charge passes through a cross-section of the conductor in 1 s, then:
the number of free electrons passing through a cross-section of the conductor in 2 s equals .......... electrons.

1. A $4.22 \times 10^{18}$
2. B $1.56 \times 10^{19}$
3. C $6.25 \times 10^{19}$
4. D $1.25 \times 10^{19}$

The coulomb equals the quantity of electric charge that ..........

1. A if it passes through a cross-section of a conductor in 5 s, the current in the conductor is 50 A
2. B if it passes through a cross-section of a conductor in 50 s, the current in the conductor is 0.5 A
3. C needs a work of 5 J to move it between two points with a potential difference of 0.5 V
4. D needs a work of 0.05 J to move it between two points with a potential difference of 0.05 V

If the work done to move $10^{20}$ electrons between the ends of conductor A is 10 J, and the work done to move $4 \times 10^{20}$ electrons between the ends of conductor B is 20 J, then the ratio between the potential differences across the two conductors $\left(\frac{V_A}{V_B}\right)$ equals ..........

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

Which of the following graphs represents the relation between the potential difference (V) across a conductor carrying a direct current and time (t)?

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

Which of the following graphs represents the relation between the work done (W) to move an electric charge between two points with a constant potential difference and the quantity of this charge (Q)?

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

In which of the following cases is the current in the resistor the greatest?

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

The opposite figure shows part of an electric circuit. If devices x, y are connected correctly, then:
these two devices are respectively ..........

1. A ammeter, ammeter
2. B ammeter, voltmeter
3. C voltmeter, ammeter
4. D voltmeter, voltmeter

The opposite figure shows part of an electric circuit. If devices x, y are connected correctly, then:
the units of the quantities measured by device x and device y respectively are ..........

1. A coulomb/second, volt
2. B coulomb/second, ampere
3. C ohm/coulomb, volt
4. D ohm/coulomb, ampere

If $6.25 \times 10^{18}$ electrons pass in two seconds through a cross-section of a conductor with a potential difference of 12 V across its ends, then the resistance of this conductor equals ..........

1. A 24 Ω
2. B 12 Ω
3. C 6 Ω
4. D 3.84 Ω

The two opposite figures (1), (2) show parts of two electric circuits carrying currents $I_1$, $I_2$ respectively. The ratio between the two currents $\left(\frac{I_1}{I_2}\right)$ equals ..........

1. A $\dfrac{4}{1}$
2. B $\dfrac{1}{4}$
3. C $\dfrac{8}{5}$
4. D $\dfrac{5}{8}$

A conductor of resistance 10 Ω carries a current of 0.5 A. If the same conductor carries a current of 1 A at the same temperature, its resistance equals ..........

1. A 2.5 Ω
2. B 5 Ω
3. C 10 Ω
4. D 20 Ω

The two opposite figures show two conductors, each carrying an electric current. If the ratio between the two currents $\left(\frac{I_1}{I_2}\right)$ is $\frac{1}{3}$, then the potential of point X equals ..........

1. A 2 V
2. B 24 V
3. C -2 V
4. D -24 V

The opposite figure shows an electric circuit carrying a current (I). One of the following changes is made to it:
(I) doubling the emf of the source
(II) halving the emf of the source
(III) doubling the value of the rheostat
(IV) halving the value of the rheostat
The current in the circuit increases to 2I in the two cases ..........

1. A (I), (II)
2. B (II), (III)
3. C (III), (IV)
4. D (I), (IV)

In the opposite circuit, when the voltage of the source is increased, the physical quantity whose value does not change is ..........

1. A the rate of flow of electrons through a cross-section of the circuit
2. B the work done by the source per second
3. C the current (I) in the circuit
4. D the value of the resistance (R)

The opposite graph shows the relation between the current through each of two wires A, B and the potential difference across each of them. Which wire has the greater electric resistance, and why?

1. A Wire A, because the slope of the line represents the resistance of the wire
2. B Wire A, because the slope of the line represents the reciprocal of the resistance of the wire
3. C Wire B, because the slope of the line represents the resistance of the wire
4. D Wire B, because the slope of the line represents the reciprocal of the resistance of the wire

The opposite graph shows the relation between the current (I) in two conductors x, y and the potential difference (V) across each of them. The ratio between the resistances of the two conductors $\left(\frac{R_x}{R_y}\right)$ equals ..........

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

Figure (1) shows the graph of the relation between the work done (W) to move an electric charge through a conductor carrying a current and the quantity of this charge (Q), and figure (2) shows the graph of the relation between the quantity of charge (Q) passing through a certain cross-section of the same conductor and time (t). The electric resistance of the conductor equals ..........

1. A 0.5 Ω
2. B 2 Ω
3. C 5 Ω
4. D 15 Ω

In the opposite circuit:
which of the following graphs represents the relation between the ammeter reading and the resistance taken from $R_V$?

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

In the opposite circuit:
which of the following graphs represents the relation between the voltmeter reading and the resistance taken from $R_V$?

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

In the opposite circuit:
which of the following graphs represents the relation between the voltmeter reading and the ammeter reading when the resistance taken from $R_V$ is changed?

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

Which of the following units is not equivalent to the watt?

1. A J/s
2. B A.V
3. C A².Ω
4. D Ω².V

In the opposite circuit:
the power consumed in the circuit is ..........

1. A 10 W
2. B 20 W
3. C 50 W
4. D 100 W

In the opposite circuit:
the energy consumed in the circuit in 20 s is ..........

1. A 100 J
2. B 200 J
3. C 400 J
4. D 1000 J

In which of the following figures is the power consumed in the resistor the greatest?

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

In the two opposite circuits, the ratio between the powers consumed in the two circuits $\left(\frac{(P_w)_2}{(P_w)_1}\right)$ is ..........

1. A $\dfrac{2}{1}$
2. B $\dfrac{4}{1}$
3. C $\dfrac{8}{1}$
4. D $\dfrac{16}{1}$

The following figures show three electric circuits x, y, z.
The correct order of the three circuits according to the power drawn from the source is ..........

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

An electric fan is labelled (220 V, 100 W) and an electric heater is labelled (220 V, 1000 W). The resistance of the heater compared with the resistance of the fan is ..........

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

In the opposite circuit, when the value of the rheostat is doubled, the rate of consumption of electrical energy in the circuit ..........

1. A doubles
2. B decreases to half
3. C decreases to a quarter
4. D stays constant

The opposite graph shows the relation between the power consumed in a conductor and the square of the current in it. The resistance of the conductor is ..........

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

Which of the following graphs represents the relation between the power consumed $(P_w)$ in a conductor carrying a direct current and time (t)?

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

Which of the following graphs represents the relation between the energy consumed (W) in a conductor carrying a direct current and time (t)?

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

The opposite figure shows an electric circuit. Which of the following graphs represents the relation between the power consumed in the resistance $R_V$ and the value of the resistance taken from it?

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

A metal wire is 20 m long, its cross-sectional area is 0.5 cm² and the resistivity of its metal is $10^{-7}$ Ω.m. The electric resistance of the wire equals ..........

1. A 0.02 Ω
2. B 0.04 Ω
3. C 0.06 Ω
4. D 0.08 Ω

An iron wire 3.14 m long with a cross-section radius of 0.5 mm is connected to a battery, so the potential difference across its ends is 5 V. If the resistivity of iron is $10^{-7}$ Ω.m, then the current in the wire equals ..........
(Given: π = 3.14)

1. A 6.2 A
2. B 8.2 A
3. C 9.6 A
4. D 12.5 A

A wire 200 m long whose material has a resistivity of $3.14 \times 10^{-7}$ Ω.m carries $2 \times 10^{19}$ electrons per second through its cross-section when it is connected to a source with a potential difference of 64 V across its terminals. The radius of the cross-section of the wire equals ..........
(Given: π = 3.14)

1. A $10^{-1}$ m
2. B $10^{-2}$ m
3. C $10^{-3}$ m
4. D $10^{-4}$ m

If the length of a copper wire is doubled and its cross-sectional area is halved, its resistance ..........

1. A doubles
2. B decreases to half
3. C increases to four times
4. D decreases to a quarter

When the length of a conductor is doubled and its cross-sectional area is halved, the resistivity of its material ..........

1. A increases four times
2. B increases three times
3. C decreases to half
4. D does not change

Three identical wires x, y, z, each connected to a potential difference (V), were kept at temperatures 3t, 2t, t respectively for a period of time. Which of these wires:
has its free electrons colliding with its atoms at a greater rate?

1. A x
2. B y
3. C z
4. D equal for the three wires

Three identical wires x, y, z, each connected to a potential difference (V), were kept at temperatures 3t, 2t, t respectively for a period of time. Which of these wires:
carries the greatest current?

1. A x
2. B y
3. C z
4. D equal for the three wires

In the opposite circuit, when the slider of the rheostat is moved from its position towards position b, which of the following choices shows what happens in the circuit?

1. A Length of the rheostat wire carrying the current: increases, current in the circuit: increases
2. B Length of the rheostat wire carrying the current: increases, current in the circuit: decreases
3. C Length of the rheostat wire carrying the current: decreases, current in the circuit: increases
4. D Length of the rheostat wire carrying the current: decreases, current in the circuit: decreases

Which of the following graphs represents the relation between the resistance (R) of several copper wires of the same length and the cross-sectional area (A) of each?

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

A group of wires have the same length; some are made of metal (x) and the others of metal (y). The opposite graph shows the relation between the electric resistance (R) and the square of the radius $(r^2)$ of the cross-section of each at the same temperature. Which of the following relations is correct when comparing the electrical conductivity (σ) of the two metals?

1. A $\sigma_x > \sigma_y$
2. B $\sigma_x < \sigma_y$
3. C $\sigma_x = \sigma_y$
4. D The answer cannot be determined

The opposite figure shows a conductor whose material has a resistivity $\rho_e$, and the cross-sectional areas of its two ends are A, 2A. The value of its resistance is ..........

1. A equal to $\dfrac{\rho_e \ell}{A}$
2. B greater than $\dfrac{\rho_e \ell}{A}$
3. C less than $\dfrac{\rho_e \ell}{A}$
4. D equal to $\dfrac{\rho_e \ell}{2A}$

If the resistivity of copper = $1.8 \times 10^{-8}$ Ω.m, then ..........

1. A the resistance of a copper conductor 1 m long with a cross-section diameter of 1 m = $1.8 \times 10^{-8}$ Ω
2. B the resistance of a copper conductor 1 m long with a cross-sectional area of 1 m² = $1.8 \times 10^{-8}$ Ω
3. C the resistance of a unit length of copper = $1.8 \times 10^{-8}$ Ω/m
4. D the resistance of a unit volume of copper = $1.8 \times 10^{-8}$ Ω/m³

If the resistivity of copper is $1.8 \times 10^{-8}$ Ω.m, which of the following represents the length and resistance of a copper wire with a cross-sectional area of 10 mm²?

1. A length 10 m and resistance $1.8 \times 10^{-8}$ Ω
2. B length 10 m and resistance 0.018 Ω
3. C length 1 m and resistance $1.8 \times 10^{-4}$ Ω
4. D length 1 m and resistance 1.8 Ω

Two wires, one of copper (Cu) and the other of iron (Fe), have the same resistance and length. The ratio between the radii of the two wires $\left(\frac{r_{Fe}}{r_{Cu}}\right)$ equals ..........

1. A $\dfrac{(\rho_e)_{Fe}}{(\rho_e)_{Cu}}$
2. B $\dfrac{(\rho_e)_{Fe}}{\sqrt{(\rho_e)_{Cu}}}$
3. C $\dfrac{\sqrt{(\rho_e)_{Fe}}}{(\rho_e)_{Cu}}$
4. D $\sqrt{\dfrac{(\rho_e)_{Fe}}{(\rho_e)_{Cu}}}$

Which of the following graphs represents the relation between the resistivity $(\rho_e)$ of a group of wires of different materials and the electrical conductivity (σ) of each?

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

Which of the following graphs expresses the relation between the electrical conductivity (σ) of a material and the cross-sectional area (A) of several conductors made of it?

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

A conductor is 106.3 cm long, its cross-sectional area is 1 mm² and its electric resistance is 1 Ω, then:
the resistivity of the conductor's material equals ..........

1. A $9.41 \times 10^{-7}$ Ω.m
2. B $8.53 \times 10^{-7}$ Ω.m
3. C $5.71 \times 10^{-6}$ Ω.m
4. D $6.25 \times 10^{-6}$ Ω.m

A conductor is 106.3 cm long, its cross-sectional area is 1 mm² and its electric resistance is 1 Ω, then:
the electrical conductivity of the conductor's material equals ..........

1. A $1.89 \times 10^{6}$ $\Omega^{-1}.m^{-1}$
2. B $2.35 \times 10^{9}$ $\Omega^{-1}.m^{-1}$
3. C $7.35 \times 10^{8}$ $\Omega^{-1}.m^{-1}$
4. D $1.06 \times 10^{6}$ $\Omega^{-1}.m^{-1}$

The following figures show four metal conductors with the same cross-sectional area, and the electrical conductivity of each conductor's material is written under its figure. Which of these conductors has the greatest resistance?

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

A power station is connected to a factory 2.5 km away by two wires. The potential difference between the ends of the two wires at the station is 240 V, the potential difference between their other ends at the factory is 220 V, and the factory uses a current of 80 A, then: (Given: π = 3.14)
the resistance of one metre of the wire equals ..........

1. A $5 \times 10^{-5}$ Ω/m
2. B $6 \times 10^{-5}$ Ω/m
3. C $12 \times 10^{-5}$ Ω/m
4. D $1 \times 10^{-4}$ Ω/m

A power station is connected to a factory 2.5 km away by two wires. The potential difference between the ends of the two wires at the station is 240 V, the potential difference between their other ends at the factory is 220 V, and the factory uses a current of 80 A, then: (Given: π = 3.14)
the radius of the wire, if the resistivity of its material is $1.57 \times 10^{-8}$ Ω.m, equals ..........

1. A 0.004 m
2. B 0.007 m
3. C 0.01 m
4. D 0.05 m

You have four wires of the same material, different in length and thickness. Each one was connected separately with the same battery and an ammeter. The ammeter has its greatest reading with the wire that is ..........

1. A long and thick
2. B long and thin
3. C short and thick
4. D short and thin

A metal wire of uniform cross-section and length (ℓ) carries a current (I) when the potential difference across its ends is (V). If a part (X) is cut from the wire and the ends of the remaining part are connected to the same potential difference (V), the current in it becomes $\left(\frac{4}{3} I\right)$. The length of the cut part (X) equals ..........

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

The opposite figure shows the lengths and cross-sectional areas of four wires made of the same material. If each one is connected to the same potential difference at the same temperature, the correct order of the wires according to the current in each is ..........

1. A c > b = d > a
2. B a > b = d > c
3. C b > a = c > d
4. D d > a = c > b

The following table shows the specifications and temperature of four conductors x, y, z, k of uniform cross-section made of the same metal. Which of these conductors has the greatest electric resistance?

1. A x: length 2 m, cross-sectional area 4 mm², temperature 20°C
2. B y: length 2 m, cross-sectional area 4 mm², temperature 50°C
3. C z: length 4 m, cross-sectional area 2 mm², temperature 20°C
4. D k: length 4 m, cross-sectional area 2 mm², temperature 50°C

A wire xyz of uniform cross-section and electric resistance (R) is connected in an electric circuit as in the opposite figure. When only switch $(K_1)$ is closed, the ammeter reading is 4 A, and when only switch $(K_2)$ is closed, the ammeter reading is 1 A. The ratio between the lengths of the two parts of the wire $\left(\frac{\ell_{xy}}{\ell_{yz}}\right)$ equals ..........

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

Three copper wires x, y, z have the same cross-sectional area. The length of x = 1 m, the length of y = 4 m and the length of z = 2 m. The ratio of the resistances of the three wires ${R_x : R_y : R_z}$ is ..........

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

Two wires (x), (y) of the same metal have the same length, and the radii of their cross-sections are $r_x$, $r_y$. Each wire is wound into a circular coil of radius $r_1$, $r_2$ respectively. The ratio between the electric resistances of the two wires $\left(\frac{R_x}{R_y}\right)$ equals ..........

1. A $\dfrac{r_y}{r_x}$
2. B $\dfrac{r_1}{r_2}$
3. C $\left(\dfrac{r_y}{r_x}\right)^2$
4. D $\left(\dfrac{r_1}{r_2}\right)^2$

Two wires of the same material: the length of the second wire is double the length of the first, and its diameter is half the diameter of the first wire. The ratio of the resistance of the second wire to the resistance of the first wire equals ..........

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

A conductor of uniform cross-section is 20 m long and its resistance is 108 Ω. Another conductor of the same material is 5 m long and its cross-sectional area is three times that of the first conductor. The resistance of the second conductor equals ..........

1. A 81 Ω
2. B 27 Ω
3. C 9 Ω
4. D 6 Ω

A cylindrical metal rod has a cross-sectional area of 2 cm² and a resistance of 22.5 Ω. If the rod is stretched uniformly until its cross-sectional area becomes 1.5 cm², its resistance becomes ..........

1. A 37 Ω
2. B 40 Ω
3. C 52 Ω
4. D 56 Ω

A metal wire is stretched uniformly until its length becomes double its original length, so its resistance becomes .......... its original value.

1. A double
2. B half
3. C four times
4. D a quarter of

A metal wire of uniform cross-section is stretched uniformly so its radius decreases by 20%. The electric resistance of the wire increases by about ..........

1. A 44%
2. B 56%
3. C 144%
4. D 244%

A cylindrical metal conductor has a cross-section diameter d and an electric resistance R. It is stretched uniformly to become a cylindrical conductor with a cross-section diameter $\frac{d}{x}$. The electric resistance of the conductor becomes ..........

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

A metal wire of uniform cross-section is stretched uniformly, and the relation between the current (I) in the wire and the potential difference (V) across its ends before and after stretching is shown in the opposite graph. The wire was stretched so that ..........

1. A its length doubled
2. B its length became nine times
3. C its cross-sectional area decreased to a third
4. D its cross-sectional area decreased to a ninth

In the opposite figure, an electric conductor is a solid cuboid. Any pair of its opposite faces can be connected to an electric source, and paths (1), (2), (3) represent the possible ways for a current to pass through the conductor. In which of these paths does the conductor have the greatest resistance to the current?

1. A Path (1)
2. B Path (2)
3. C Path (3)
4. D All paths have the same electric resistance

An electric conductor in the shape of a solid cuboid is connected in two different ways to a battery of negligible internal resistance, as in circuits (1), (2). The ratio between the currents in the two circuits $\left(\frac{I_1}{I_2}\right)$ equals ..........

1. A $\dfrac{A_1}{A_2}$
2. B $\left(\dfrac{A_1}{A_2}\right)^2$
3. C $\dfrac{A_2}{A_1}$
4. D $\left(\dfrac{A_2}{A_1}\right)^2$

A metal wire has a volume of $2 \times 10^{-4}$ m³, a cross-sectional area of $4 \times 10^{-5}$ m² and a resistance of 1.25 Ω. The electrical conductivity of the metal equals ..........

1. A $10^{3}$ $\Omega^{-1}.m^{-1}$
2. B $10^{5}$ $\Omega^{-1}.m^{-1}$
3. C $10^{7}$ $\Omega^{-1}.m^{-1}$
4. D $10^{8}$ $\Omega^{-1}.m^{-1}$

A metal cube has a side length ℓ. When two opposite faces are connected to the ends of an electric circuit, its electric resistance is R. The electrical conductivity (σ) of this metal can be found from the relation ..........

1. A $\sigma = R\ell$
2. B $\sigma = \dfrac{\pi}{R\ell}$
3. C $\sigma = \dfrac{1}{2R\ell}$
4. D $\sigma = \dfrac{1}{R\ell}$

Two copper wires: the first is 10 m long with a mass of 0.1 kg, and the second is 40 m long with a mass of 0.2 kg. The ratio between their resistances $\left(\frac{R_1}{R_2}\right)$ equals ..........

1. A $\dfrac{1}{4}$
2. B $\dfrac{1}{5}$
3. C $\dfrac{1}{7}$
4. D $\dfrac{1}{8}$

In the figure shown, two wires x, y are made of the same material. If the mass of wire x is 5 g and the mass of wire y is 10 g, then the ratio between the resistances of the two wires $\left(\frac{R_x}{R_y}\right)$ equals ..........

1. A $\dfrac{2}{1}$
2. B $\dfrac{4}{1}$
3. C $\dfrac{8}{1}$
4. D $\dfrac{16}{1}$

In the opposite figure, a conductor 3.14 m long, whose cross-section is a semicircle of diameter 2 mm, carries an electric current. If the resistivity of the conductor's material is $10^{-6}$ Ω.m, its electric resistance equals ..........
(Given: π = 3.14)

1. A 0.25 Ω
2. B 0.5 Ω
3. C 1 Ω
4. D 2 Ω

A hollow cylinder made of a metal of resistivity $2 \times 10^{-8}$ Ω.m is 1 m long, its inner radius is 1 mm and its outer radius is 2 mm, as in the opposite figure. The electric resistance between the two ends of the cylinder equals ..........

1. A $1.6 \times 10^{-3}$ Ω
2. B $2.1 \times 10^{-3}$ Ω
3. C $4.8 \times 10^{-3}$ Ω
4. D $8 \times 10^{-3}$ Ω

The opposite graph shows the relation between the resistance of a wire (R) and its length (ℓ). If the cross-sectional area of the wire is 0.1 cm², then:
the resistivity of the material of this wire $(\rho_e)$ equals ..........

1. A $3 \times 10^{-7}$ Ω.m
2. B $5 \times 10^{-6}$ Ω.m
3. C $4 \times 10^{-5}$ Ω.m
4. D $9 \times 10^{-8}$ Ω.m

The opposite graph shows the relation between the resistance of a wire (R) and its length (ℓ). If the cross-sectional area of the wire is 0.1 cm², then:
the resistance of a 25 m long piece of the wire equals ..........

1. A 9.25 Ω
2. B 11.3 Ω
3. C 12.5 Ω
4. D 15.9 Ω

The opposite graph shows the relation between the resistance (R) and the length (ℓ) for two groups of wires x, y made of copper. The ratio between the cross-sectional areas of the two groups of wires $\left(\frac{A_x}{A_y}\right)$ is ..........

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

The opposite graph shows the relation between the potential difference (V) across a wire 5 m long with a cross-sectional area of 0.1 mm² and the current (I) in it. The electrical conductivity of the material of this wire equals ..........

1. A $4.1 \times 10^{6}$ $\Omega^{-1}.m^{-1}$
2. B $3.2 \times 10^{5}$ $\Omega^{-1}.m^{-1}$
3. C $2.5 \times 10^{6}$ $\Omega^{-1}.m^{-1}$
4. D $1.6 \times 10^{5}$ $\Omega^{-1}.m^{-1}$

The opposite graph shows the relation between the potential difference (V) and the current (I) in two wires A, B of the same material:
if the two wires have the same length and the cross-sectional area of wire B is $3 \times 10^{-6}$ m², then the cross-sectional area of wire A equals ..........

1. A $10^{-6}$ m²
2. B $9 \times 10^{-6}$ m²
3. C $3 \times 10^{-6}$ m²
4. D $12 \times 10^{-8}$ m²

The opposite graph shows the relation between the potential difference (V) and the current (I) in two wires A, B of the same material:
if the two wires have the same cross-sectional area and the length of wire B is 3 m, then the length of wire A equals ..........

1. A 1 m
2. B 2 m
3. C 3 m
4. D 9 m

The graph shown represents the relation between the potential difference (V) across two wires x, y of the same length and the current (I) in each of them at constant temperature. If the ratio between the cross-sectional areas of the two wires $\left(\frac{A_x}{A_y}\right)$ is $\frac{12}{25}$, then the ratio between the resistivities of their materials $\left(\frac{(\rho_e)_x}{(\rho_e)_y}\right)$ equals ..........

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

The opposite table shows different values of lengths, cross-sectional areas and resistivities of wires made of different materials:
which of these wires carries a current of 2 A when the potential difference across its ends is 10 V?

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

The opposite table shows different values of lengths, cross-sectional areas and resistivities of wires made of different materials:
which of these wires gives a greater quantity of heat than the other wires when the same current passes through them for the same time?

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

The opposite table shows different values of lengths, cross-sectional areas and resistivities of wires made of different materials:
which of these wires gives a smaller heat power than the other wires when each is connected to the same potential difference?

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

Two conductors xy, zk of uniform cross-section are made of the same metal. The length of xy = ℓ and the length of zk = 2ℓ, and each is connected in an electric circuit as in the two following figures.
If the electric power consumed in the two conductors is equal, then the ratio between their cross-sectional areas $\left(\frac{A_{xy}}{A_{zk}}\right)$ equals ..........

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

A wire of resistance R consumes an electric power $P_w$ when the potential difference across its ends is V. If the wire is stretched uniformly so that its length doubles, and its ends are connected to the same potential difference V, the wire consumes an electric power of ..........

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

A wire is 2 m long and its cross-sectional area is $4 \times 10^{-6}$ m². If the potential difference across its ends is 20 V, the power consumed in it is 10 W, then:
the resistivity of its material equals ..........

1. A $2 \times 10^{-7}$ Ω.m
2. B $10^{-5}$ Ω.m
3. C $8 \times 10^{-5}$ Ω.m
4. D $4 \times 10^{-6}$ Ω.m

A wire is 2 m long and its cross-sectional area is $4 \times 10^{-6}$ m². If the potential difference across its ends is 20 V, the power consumed in it is 10 W, then:
the number of electrons passing through its cross-section in one minute equals .......... electrons.

1. A $9.741 \times 10^{17}$
2. B $6.435 \times 10^{18}$
3. C $2.314 \times 10^{19}$
4. D $1.875 \times 10^{20}$

Explain why some solids conduct electric current, while others are electrical insulators.

An electric current of 3.2 mA passes through a wire. Calculate the rate of flow of electrons through a cross-section of the wire.

The opposite figure shows a heater wire carrying a direct current. Explain why the current at the two ends of the wire is equal, even though electrical energy is consumed in it.

The opposite graph shows the relation between the quantity of charge (Q) passing through a certain cross-section of a conductor and time (t). Find the ratio between the currents in the conductor during the two stages ab, bc respectively.

Explain why neither of the two lamps x, y lights up, even though each is connected to a dry cell as in the opposite figure.

In the opposite figure, if the work done to move $10^{20}$ free electrons from point y to point x is 80 J, calculate the electric potential at point y.

An electric lamp whose filament has a resistance of $1.6\ \Omega$ is connected to a potential difference of 9 V. Calculate the number of electrons passing per minute through a cross-section of the lamp filament.

In the opposite circuit, a battery of negligible internal resistance is connected to two lamps x, y through two switches $K_1$, $K_2$ respectively, an ammeter and a voltmeter. If the resistance of lamp y is greater than the resistance of lamp x, explain what happens to the reading of each of the ammeter and the voltmeter when switch $K_1$ is opened and switch $K_2$ is closed.

Two metal wires: the first has a resistance R and $10^{20}$ electrons pass through its cross-section per second, and the second has a resistance 2R and $2 \times 10^{20}$ electrons pass through its cross-section per second. Calculate the ratio between the power consumed in the first wire and the power consumed in the second wire.

The coil of an electric heater used to heat water is connected to a 220 V source of negligible internal resistance. What is the effect of removing the heater coil and using another coil of higher electric resistance on the rate of heating the water? Why?

In figures (1), (2), if the power consumed in the two resistors $R_1$, $R_2$ is equal, and the ratio between the readings of the two ammeters $\frac{A_1}{A_2}$ is $\frac{1}{2}$:
(1) Find the ratio between the readings of the two voltmeters $\frac{V_1}{V_2}$
(2) Explain why the readings of the two voltmeters $V_1$, $V_2$ and of the two ammeters $A_1$, $A_2$ cannot be used to verify Ohm's law.

A student used the tools shown in the figure to study how the resistance of a wire (AB) of uniform cross-section changes with its length:
(1) What is the role of end (X) in achieving the aim of the experiment?
(2) What is the purpose of using the two devices Z, M?

How can you increase the electric resistance of a certain copper wire at a certain temperature?

What physical quantity is measured by each of the following units:
(1) ampere.second? (2) volt.coulomb? (3) volt.ampere⁻¹?
(4) joule / ohm.coulomb? (5) volt.second.ohm⁻¹?

Write the mathematical relation represented by each graph and what the slope of the straight line represents in each of the following:
where: (Q) is the quantity of electric charge, (W) the work, (R) the resistance of the conductor, (ℓ) the length of the conductor, (A) the cross-sectional area of the conductor, (r) the radius of the conductor.

The opposite table gives the specifications of three metal conductors with the same cross-sectional area made of different materials (x, y, z). If σ stands for the electrical conductivity of the material:
x: length 2 m, resistance $1\ \Omega$
y: length 3 m, resistance $4\ \Omega$
z: length 3 m, resistance $6\ \Omega$
(1) Find the ratio $\sigma_x : \sigma_y : \sigma_z$
(2) Which of these materials is preferred for making electrical connecting wires? Explain your answer.

A solid cube of side 10 cm made of a conducting material of resistivity $10^{-7}\ \Omega m$ is reshaped into a cylindrical wire of resistance $20\ \Omega$. Calculate the length of the wire.

A wire is 2 m long and its resistance is $2\ \Omega$. If the density of the wire's material is $7000\ kg/m^3$ and its resistivity is $10^{-6}\ \Omega m$, calculate the mass of the wire.

A group of wires made of the same material, each 12 m long. The opposite graph shows the relation between the resistance (R) of each wire and the reciprocal of its cross-sectional area $\frac{1}{A}$. Find:
(1) the electric resistance of a wire of the same material and the same length with a cross-sectional area of $0.0025\ cm^2$
(2) the electrical conductivity of the material of the wires.

The opposite graph shows the relation between the current (I) in two wires x, y of uniform cross-section, made of the same material and of the same length, and the potential difference (V) across each of them. Which wire is thicker? Why?

The opposite figure shows a closed insulated space containing two coils. After closing switch K connected to coil (1) for a while, the reading of ammeter (A) connected to coil (2) was seen to decrease. How do you explain that?

Electric lamp A has a power of 80 W and works on a potential difference of 220 V, and electric lamp B has a power of 20 W and works on a potential difference of 24 V. If the filaments of the two lamps are made of the same material and have the same length, calculate the ratio between the radii of the two filaments $\frac{r_A}{r_B}$

The electric current through a metal conductor connected to the terminals of a voltage source results from the flow of .......... (2nd session 2025)

1. A free electrons from the end of lower electric potential to the end of higher potential
2. B free electrons from the end of higher electric potential to the end of lower potential
3. C positive ions from the end of lower electric potential to the end of higher potential
4. D positive ions from the end of higher electric potential to the end of lower potential

A simple electric circuit consists of a battery and an ohmic resistor as shown in the figure. Which of the following choices correctly describes the relation between the electric potentials of the points shown (W), (X), (Y), (Z)? (Sample exam 2026)

1. A The potential of W is greater than that of Z, and the potential of X is less than that of Y
2. B The potential of W is less than that of Z, and the potential of X is greater than that of Y
3. C The potential of W is greater than that of Z, and the potential of X is greater than that of Y
4. D The potential of W is less than that of Z, and the potential of X is less than that of Y

The opposite graph shows the relation between the power consumed $(P_w)$ in a conductor and the square of the current $(I^2)$ in this conductor. The slope of the line representing the relation equals .......... (Sample exam 2025)

1. A the resistance of the conductor
2. B the reciprocal of the resistance of the conductor
3. C the potential difference across the conductor
4. D the square of the potential difference across the conductor

An electric lamp labelled (80 W, 100 V) means that .......... (Sample exam 2025)

1. A the electric resistance of the lamp is $0.8\ \Omega$
2. B the electric resistance of the lamp is $1.25\ \Omega$
3. C when the potential difference across the lamp is 100 V, a current of 0.8 A passes through it
4. D when the potential difference across the lamp is 100 V, a current of 1.25 A passes through it

If the work done to move a charge of 2 C inside and outside the source is 12 J, this means that .......... (1st session 2025)

1. A the opposition of the source to the current is $6\ \Omega$
2. B the current through the source is 6 A
3. C the electric power produced by the source is 6 W
4. D the emf of the source is 6 V

You have two copper wires of the same length. If the cross-sectional area of the second wire is three times that of the first, then the ratio between the resistance of the first wire and the resistance of the second wire $\frac{R_1}{R_2}$ equals .......... (Trial exam / May 2021)

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

In front of you are four conductors of uniform cross-section made of the same material with different dimensions. The order of these conductors in ascending order of their electric resistances is .......... (Trial exam / May 2021)

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

A conductor of length ℓ and cross-sectional area 3A has a potential difference V applied across its ends, so a current I passes through it. If another conductor of the same material is connected to the same potential difference V, the current in it becomes 3I. The length and cross-sectional area of the second conductor are .......... (Trial exam / June 2021)

1. A length 2ℓ, area 18A
2. B length 3ℓ, area 3A
3. C length 18ℓ, area 2A
4. D length $\frac{1}{3}$ℓ, area $\frac{1}{3}$A

Two wires of the same material: the diameter of the first wire is three times the diameter of the second, and the resistance of the second wire is four times the resistance of the first. The length of the second wire is .......... the length of the first wire. (1st session 2021)

1. A $\frac{4}{3}$
2. B $\frac{4}{9}$
3. C $\frac{36}{1}$
4. D $\frac{12}{1}$

A current I passes through a conductor of length ℓ and cross-sectional area A. When the battery used is changed, the current in the same conductor becomes 3I. The cross-sectional area of the conductor in this case is .......... (2nd session 2021)

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

Two wires (1) and (2) are made of the same material. Wire (1) has a length 3ℓ and a radius (r), while wire (2) has a length 2ℓ and a radius (2r), as shown in the figure. The ratio $\frac{I_1}{I_2}$ = .......... (1st session 2022)

1. A $\frac{12}{1}$
2. B $\frac{1}{12}$
3. C $\frac{3}{2}$
4. D $\frac{1}{6}$

The opposite graph shows the relation between the electric resistance (R) of several groups of wires of equal length, each group made of a different material, and the reciprocal of the wire's volume $\frac{1}{V_{ol}}$ in each group. The order of the electrical conductivity (σ) of the materials of the groups of wires is .......... (2nd session 2022)

1. A $\sigma_4 > \sigma_1 > \sigma_3 > \sigma_2$
2. B $\sigma_1 > \sigma_3 > \sigma_2 > \sigma_4$
3. C $\sigma_1 > \sigma_2 > \sigma_3 > \sigma_4$
4. D $\sigma_4 > \sigma_3 > \sigma_2 > \sigma_1$

Two groups X, Y of wires have the same length, and each group is made of a different metal. The opposite graph shows the relation between the electric resistance (R) of the wire and the reciprocal of its cross-sectional area $\frac{1}{A}$. Which of the following choices is correct when comparing the two metals? (Trial exam 2023)

1. A The metal of group X has a greater resistivity
2. B The metal of group Y has a greater resistivity
3. C The metal of group X has a greater electrical conductivity
4. D The electrical conductivities of the two metals are equal

You have four wires (1), (2), (3), (4) made of different materials as shown in the following figures. Which of these wires has the material with the highest electrical conductivity at the same temperature? (1st session 2023)

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

You have four aluminium wires as in the following figures. Which of these wires has the smallest electric resistance? (2nd session 2023)

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

The figure shows a metal conductor with two parts A, B of uniform cross-section, equal in length and different in cross-sectional area, with electric resistances $R_A$, $R_B$ respectively. If the conductor is connected across a battery in a closed circuit, the ratio $\frac{V_A}{V_B}$ = .......... (1st session 2024)

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

Wires of different lengths made of three different materials x, y, z have the same cross-sectional area and are at the same temperature. The opposite graph shows the relation between the electric resistance (R) of the wires and the length (ℓ) of each. If $\sigma_x$, $\sigma_y$, $\sigma_z$ represent the electrical conductivities of the wires' materials, which of the following choices is correct? (1st session 2024)

1. A $\sigma_z = \sigma_y = \sigma_x$
2. B $\sigma_z < \sigma_y < \sigma_x$
3. C $\sigma_z > \sigma_y > \sigma_x$
4. D $\sigma_z > \sigma_x > \sigma_y$

Figure (1) shows an electric circuit containing a conductor AB at temperature $T_1$, and the voltmeter reading was $V_1$. If the temperature of conductor AB is raised to $T_2$ and then kept constant, the voltmeter reading becomes $V_2$ as in figure (2). Which of the following choices is correct? (2nd session 2024)

1. A The voltmeter reading $V_2$ = zero
2. B The voltmeter reading $V_1$ = the voltmeter reading $V_2$
3. C The voltmeter reading $V_1$ is less than the voltmeter reading $V_2$
4. D The voltmeter reading $V_1$ is greater than the voltmeter reading $V_2$

Two groups (A), (B) of wires have the same cross-sectional area, are at the same temperature and are made of two different materials. The opposite graph shows the relation between the electric resistance (R) of each of these wires and its length (ℓ). Which of the following graphs are correct? (2nd session 2024)

1. A Graph (1) and graph (3)
2. B Graph (2) and graph (4)
3. C Graph (1) and graph (4)
4. D Graph (2) and graph (3)

A battery of emf $V_B$ and negligible internal resistance is connected to a resistance wire ab of uniform cross-section that is not insulated, a voltmeter and a slider as in the opposite figure. While the slider is moved from point a to point b, the voltmeter reading .......... (Sample exam 2025)

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

Two long copper wires x, y differ in thickness, and the length taken from each can be changed. The opposite graph shows the relation between the resistance (R) and the length (ℓ) taken from each wire. The ratio between the cross-sectional areas of the two wires $\frac{A_x}{A_y}$ is .......... (Sample exam 2025)

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

The opposite graph shows the relation between the electric resistance (R) of a group of wires of the same material, each with a cross-sectional area of $0.1\ cm^2$, and the length (ℓ) of each of these wires. The resistivity of the material of these wires $(\rho_e)$ equals .......... (Sample exam 2025)

1. A $2.4 \times 10^{-7}\ \Omega m$
2. B $3.6 \times 10^{-7}\ \Omega m$
3. C $1.2 \times 10^{-6}\ \Omega m$
4. D $1.6 \times 10^{-6}\ \Omega m$

Which of the following changes increases the electric resistance of a metal wire? (1st session 2025)

1. A Decreasing the cross-sectional area of the wire
2. B Lowering the temperature of the wire
3. C Decreasing the length of the wire
4. D Covering the wire with an insulating layer

In the following figure, three wires (X, Y, Z) of the same metal have lengths (ℓ, 2ℓ, ℓ) and cross-sectional areas (2A, A, A) respectively. If the resistance of wire (X) is R, then the resistances of wires (Y), (Z) are .......... (2nd session 2025)

1. A resistance of Y = 2R, resistance of Z = 4R
2. B resistance of Y = 8R, resistance of Z = 4R
3. C resistance of Y = R, resistance of Z = 2R
4. D resistance of Y = 4R, resistance of Z = 2R

An electric conductor 1 m long with a cross-sectional area of $2\ mm^2$ carries a current of 2 A when the potential difference across its ends is 6 V. This means that .......... (Sample exam 2026)

1. A the electric power consumed by the conductor is 3 W
2. B the resistivity of the conductor's material is $6 \times 10^{6}\ \Omega m$
3. C the electrical conductivity of the conductor's material is $1.667 \times 10^{5}\ \Omega^{-1} m^{-1}$
4. D the electric resistance of the conductor is $12\ \Omega$