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Current Electricity Set-6

Practice Important MCQs for Current Electricity — Physics, Class 12.

Current electricity is central to CBSE Class 12 and also forms the base for many JEE/NEET questions involving drift current, internal resistance, combinations of cells, and effective resistance/power in circuits. Mastery of these concepts helps you solve both numerical and conceptual problems quickly and accurately.

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Q1. A copper wire of radius $1.0\ \text{mm}$ carries a steady current of $5.0\ \text{A}$ . The free electron density in copper is $n=8.5\times10^{28}\ \text{m}^{-3}$ and the elementary charge is $e=1.6\times10^{-19}\ \text{C}$ . Using $I = n e A v_{\text{d}}$ , estimate the drift speed $v_{\text{d}}$ of electrons in the wire.

(A)

$1.17\times10^{-3}\ \mathrm{m\ s^{-1}}$

(B)

$1.17\times10^{-5}\ \mathrm{m\ s^{-1}}$

(C)

$1.17\times10^{-4}\ \mathrm{m\ s^{-1}}$

(D)

$1.17\times10^{-1}\ \mathrm{m\ s^{-1}}$

Q2. A conductor in the shape of a right circular cone of length $L$ has radius $r_0$ at one end and radius $2r_0$ at the other. Its resistivity is $\rho$ and current flows along the axis between the two ends. By writing $R=\int \rho\,\mathrm{d}x/A(x)$ and using the linear variation of radius, the resistance between the ends is:

(A)

$\displaystyle \frac{\rho L}{2\pi r_0^2}$

(B)

$\displaystyle \frac{\rho L}{3\pi r_0^2}$

(C)

$\displaystyle \frac{\rho L}{\pi r_0^2}$

(D)

$\displaystyle \frac{2\rho L}{3\pi r_0^2}$

Q3. Two cells with emfs $E_1=1.50\ \text{V}$ , $E_2=1.20\ \text{V}$ and internal resistances $r_1=0.50\ \Omega$ , $r_2=0.30\ \Omega$ are connected in parallel and the combination is connected across an external resistor $R=2.0\ \Omega$ . What is the magnitude of the current through $R$ ? (Treat the parallel cells correctly by finding the equivalent Thevenin emf and internal resistance.)

(A)

$0.30\ \text{A}$

(B)

$0.75\ \text{A}$

(C)

$0.45\ \text{A}$

(D)

$0.60\ \text{A}$

Q4. Two identical cells each of emf $E$ and internal resistance $r$ are used to drive an external resistor $R$ . Let $P_{\text{series}}$ be the power delivered to $R$ when the cells are connected in series, and $P_{\text{parallel}}$ the power when they are connected in parallel. Which statement is correct?

(A)

$P_{\text{series}}>P_{\text{parallel}}$ for every value of $R$ .

(B)

$P_{\text{series}}>P_{\text{parallel}}$ if $R>r$ , $P_{\text{parallel}}>P_{\text{series}}$ if $R<r$ , and $P_{\text{series}}=P_{\text{parallel}}$ when $R=r$ .

(C)

$P_{\text{parallel}}>P_{\text{series}}$ if $R>r$ , and reverse if $R<r$ .

(D)

$P_{\text{series}}=P_{\text{parallel}}$ for all $R$ only if $E=0$ .

Q5. In a potentiometer experiment with a uniform wire and a driver of fixed emf, a test cell of emf $1.00\ \text{V}$ gives a balancing length $l_1=40.0\ \text{cm}$ when connected open-circuit. When a load resistor $R_L=10.0\ \Omega$ is connected across the test cell, the balancing length becomes $l_2=32.0\ \text{cm}$ . Assuming the potential gradient along the wire is unchanged, the internal resistance $r$ of the test cell is:

(A)

$2.5\ \Omega$

(B)

$1.9\ \Omega$

(C)

$3.3\ \Omega$

(D)

$2.0\ \Omega$

Q6. A copper wire of radius $0.50\ \mathrm{mm}$ carries a steady current of $5.0\ \mathrm{A}$ . The free electron number density in copper is $n=8.5\times10^{28}\ \mathrm{m^{-3}}$ . Using $I=neAv_{d}$ , the order of magnitude of the drift speed $v_{d}$ of electrons in the wire is closest to

(A)

$4.7\times10^{-6}\ \mathrm{m\ s^{-1}}$

(B)

$4.7\times10^{-3}\ \mathrm{m\ s^{-1}}$

(C)

$4.7\times10^{-4}\ \mathrm{m\ s^{-1}}$

(D)

$4.7\times10^{-2}\ \mathrm{m\ s^{-1}}$

Q7. Two straight uniform wires made of the same material have equal mass. Wire A has length $L$ and radius $r$ . Wire B has length $2L$ . Each wire is separately connected across the same potential difference $V$ . If $I_A$ and $I_B$ are the currents through A and B respectively, the ratio $I_B/I_A$ is

(A)

$\dfrac{1}{4}$

(B)

$\dfrac{1}{2}$

(C)

$2$

(D)

$4$

Q8. A battery of emf $12.0\ \mathrm{V}$ and internal resistance $1.0\ \Omega$ is connected in series with resistors $R_{1}=2.0\ \Omega$ and $R_{2}=3.0\ \Omega$ . A voltmeter of resistance $R_{v}=48.0\ \Omega$ is placed across $R_{2}$ . The reading of the voltmeter (in volts) is approximately

(A)

$6.00\ \mathrm{V}$

(B)

$4.50\ \mathrm{V}$

(C)

$8.00\ \mathrm{V}$

(D)

$5.82\ \mathrm{V}$

Q9. Two identical filament bulbs, each of resistance $R$ , are connected in parallel across a battery of emf $E$ and internal resistance $r$ . Initially both bulbs glow. One filament fuses (becomes open) leaving the other intact. If $P_{i}$ is the power dissipated in one bulb before fusing and $P_{f}$ is the power dissipated in the remaining bulb after fusing, which statement is correct?

(A)

$P_{f}=2P_{i}$ (the remaining bulb becomes twice as bright)

(B)

$P_{f}=P_{i}\left(\dfrac{r+R}{2r+R}\right)^{2}$

(C)

$P_{f}=P_{i}\left(\dfrac{2r+R}{r+R}\right)^{2}$

(D)

$P_{f}=P_{i}$ (brightness of the remaining bulb remains unchanged)

Q10. Twelve identical resistors each of resistance $R$ are placed along the edges of a cube. The equivalent resistance between two opposite vertices of the cube (across the space diagonal) is

(A)

$\dfrac{5R}{6}$

(B)

$\dfrac{R}{2}$

(C)

$\dfrac{2R}{3}$

(D)

$\dfrac{3R}{4}$

Q11. A battery of emf $12\ \mathrm{V}$ and internal resistance $2\ \Omega$ is connected to an external resistor of $4\ \Omega$ . The heat produced per second (power dissipated) inside the battery due to its internal resistance is:

(A)

$6\ \mathrm{W}$

(B)

$8\ \mathrm{W}$

(C)

$12\ \mathrm{W}$

(D)

$4\ \mathrm{W}$

Q12. A battery of emf $E$ and internal resistance $r$ is connected to a variable resistor $R$ in series with two identical resistors each of resistance $R_0$ that are connected in parallel (the two $R_0$ are in parallel and that combination is in series with $R$ ). For what value of $R$ is the power dissipated in the variable resistor $R$ maximum?

(A)

$R = r$

(B)

$R = r + R_0$

(C)

$R = \dfrac{R_0}{2}$

(D)

$R = r + \dfrac{R_0}{2}$

Q13. Two identical cells, each of emf $E$ and internal resistance $r$ , are used to drive a load resistor $R$ . Compare the power dissipated in $R$ when (I) a single cell is used and (II) the two cells are connected in series across the same $R$ . Which statement is correct?

(A)

The power with two cells in series is greater than with a single cell but less than $4$ times the single-cell power (i.e., lies between $1\times$ and $4\times$ ).

(B)

The power with two cells in series is always exactly $4$ times the single-cell power.

(C)

The power with two cells in series is always exactly $2$ times the single-cell power.

(D)

The power with two cells in series is always less than the power with a single cell.

Q14. A cylindrical conductor of length $L$ has uniform resistivity $\rho$ , but its cross-sectional area varies linearly from $A_0$ at one end ( $x=0$ ) to $2A_0$ at the other end ( $x=L$ ). The resistance between the two ends is:

(A)

$\dfrac{\rho L}{2A_0}\,\ln 2$

(B)

$\dfrac{\rho L}{A_0}\,\dfrac{1}{\ln 2}$

(C)

$\dfrac{\rho L}{A_0}\,\ln 2$

(D)

$\dfrac{3\rho L}{2A_0}$

Q15. Consider an infinite network of identical resistors (each of resistance $R$ ) connected between terminals $A$ and $B$ as follows: from $A$ a resistor $R$ connects to node 1; from node 1 another resistor $R$ connects to node 2; and so on ad infinitum. Additionally, from each node there is a resistor $R$ that connects directly to terminal $B$ . The equivalent resistance between $A$ and $B$ is:

(A)

$\dfrac{\sqrt{5}-1}{2}\,R$

(B)

$\dfrac{1+\sqrt{5}}{2}\,R$

(C)

$\dfrac{1+\sqrt{17}}{2}\,R$

(D)

$2R$

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