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Current Electricity Set-3 MCQ Online Practice Test | Class 12 | Quiz Tweek

Current Electricity Set-3

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

Current Electricity is central to both CBSE board exams and competitive tests because it connects microscopic charge motion to macroscopic circuit behaviour: topics such as Ohm’s law, resistivity, internal resistance of cells, and Kirchhoff’s laws form the backbone of circuit analysis problems that appear frequently in board papers and JEE/NEET. Mastery of this chapter develops algebraic and conceptual skills needed to analyze multi-loop circuits, non-ideal measuring instruments, and power transfer — skills that are repeatedly tested in higher‑order problems.

Beyond routine calculations, Current Electricity trains students to interpret experimental graphs (V–I, resistivity vs temperature), reason about the effect of geometry and temperature on resistance, and apply conservation laws in nontrivial configurations (cells in series/parallel, potentiometer setups, meter‑bridge). These competencies are essential for solving multi-step JEE/NEET style questions and for writing clear, logical solutions in board exams.

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Q1. Two wires X and Y of equal length $L$ and cross-sectional area $A$ have resistivities near temperature $T_0$ given by

\rho_X(T)=\rho_0[1+\alpha(T-T_0)],\qquad \rho_Y(T)=\rho_0\exp[-\beta(T-T_0)],

with $\alpha,\beta>0$ and $\rho_X(T_0)=\rho_Y(T_0)=\rho_0$ . At $T_0$ both wires carry the same current $I$ . For a small increase $\Delta T>0$ (first‑order in $\Delta T$ ), which statement about the change in Joule heating $P=I^2R$ in the two wires is correct?

(A)

Option A: Power in X increases approximately by $I^2\frac{\rho_0\alpha L}{A}\Delta T$ , and power in Y also increases approximately by $I^2\frac{\rho_0\beta L}{A}\Delta T$ .

(B)

Option B: Power in both X and Y decrease linearly with $\Delta T$ .

(C)

Option C: Power in X increases by approximately $I^2\frac{\rho_0\alpha L}{A}\Delta T$ , whereas power in Y decreases by approximately $I^2\frac{\rho_0\beta L}{A}\Delta T$ (to first order in $\Delta T$ ).

(D)

Option D: Power in X increases approximately by $I^2\frac{\rho_0\alpha L}{A}\Delta T$ , while power in Y remains unchanged to first order in $\Delta T$ .

Q2. A battery has emf $E=12\ \text{V}$ and internal resistance $r=2\ \Omega$ . When connected to an external resistor $R$ the steady current is $2.0\ \text{A}$ . The value of $R$ is

(A)

Option A: $3\ \Omega$

(B)

Option B: $4\ \Omega$

(C)

Option C: $6\ \Omega$

(D)

Option D: $8\ \Omega$

Q3. A copper wire of radius $1.0\ \text{mm}$ carries a steady current $I=5.0\ \text{A}$ . With electron density $n=8.5\times10^{28}\ \text{m}^{-3}$ and electron charge $e=1.6\times10^{-19}\ \text{C}$ , the magnitude of the drift speed $v_d$ of electrons in the wire is closest to

(A)

Option A: $1.17\times10^{-4}\ \text{m s}^{-1}$

(B)

Option B: $1.17\times10^{-3}\ \text{m s}^{-1}$

(C)

Option C: $1.17\times10^{-5}\ \text{m s}^{-1}$

(D)

Option D: $1.17\times10^{-6}\ \text{m s}^{-1}$

Q4. Assertion: If two cells of emf $E_1$ and $E_2$ with internal resistances $r_1$ and $r_2$ are connected in series opposing, the equivalent emf is $|E_1-E_2|$ and the equivalent internal resistance is $|r_1-r_2|$ .

Reason: When cells are connected in series their emfs add algebraically (opposing gives a difference), but the internal resistances always add ( $r_{\rm eq}=r_1+r_2$ ) irrespective of polarity.

(A)

Option A: Both Assertion and Reason are true and Reason is the correct explanation of the Assertion.

(B)

Option B: Both Assertion and Reason are true but Reason is NOT the correct explanation of the Assertion.

(C)

Option C: Assertion is true but Reason is false.

(D)

Option D: Assertion is false but Reason is true.

Q5. A cell with emf $E=12\ \text{V}$ and internal resistance $r=3\ \Omega$ supplies a variable external resistance $R$ . The power delivered to $R$ is $P(R)=\dfrac{E^2R}{(R+r)^2}$ and the $P$ vs $R$ curve has a single maximum. The value of $R$ at the peak and the maximum power $P_{\rm max}$ are:

(A)

Option A: $R=1.5\ \Omega,\;P_{\rm max}=6\ \text{W}$

(B)

Option B: $R=6\ \Omega,\;P_{\rm max}=12\ \text{W}$

(C)

Option C: $R=3\ \Omega,\;P_{\rm max}=12\ \text{W}$

(D)

Option D: $R=3\ \Omega,\;P_{\rm max}=24\ \text{W}$

Q6. A uniform cylindrical conductor has length $L=1.0\ \text{m}$ , cross-sectional area $A=1.0\ \text{mm}^2$ , and resistivity $\rho=1.6\times10^{-8}\ \Omega\cdot\text{m}$ . Its electrical resistance is

(A)

Option A: $A=1.0\ \text{mm}^2$

(B)

Option B: $1.6\times10^{-3}\ \Omega$

(C)

Option C: $1.6\times10^{-1}\ \Omega$

(D)

Option D: $1.6\times10^{-4}\ \Omega$

Q7. A battery of emf $E=12\ \text{V}$ and internal resistance $r=2\ \Omega$ is connected in series with an ammeter of internal resistance $r_A=1\ \Omega$ and an external resistor $R=6\ \Omega$ . A voltmeter of internal resistance $r_V=4\ \Omega$ is connected across $r_A=1\ \Omega$ to measure the potential difference across $R$ . The voltmeter will read (rounded to two decimal places)

(A)

Option A: $4.00\ \text{V}$

(B)

Option B: $5.33\ \text{V}$

(C)

Option C: $6.00\ \text{V}$

(D)

Option D: $2.67\ \text{V}$

Q8. Assertion: In a uniform steady conducting wire connected to a DC source the current density $\mathbf{J}$ is the same at all cross-sections.

Reason: Charge conservation (Kirchhoff's current law) in steady state implies net current through any cross-section is the same; for a uniform cross-section this means $\mathbf{J}$ is the same everywhere.

(A)

Option A: Both Assertion and Reason are true and Reason is the correct explanation of the Assertion.

(B)

Option B: Both Assertion and Reason are true but Reason is NOT the correct explanation of the Assertion.

(C)

Option C: Assertion is true but Reason is false.

(D)

Option D: Assertion is false but Reason is true.

Q9. Two cells with emfs $E_1=1.5\ \text{V},\ r_1=1.0\ \Omega$ and $E_2=1.2\ \text{V},\ r_2=2.0\ \Omega$ are connected in parallel (positive to positive) and then connected to an external load $R=10\ \Omega$ . The current through the load (approx.) is

(A)

Option A: $0.014\ \text{A}$

(B)

Option B: $0.90\ \text{A}$

(C)

Option C: $1.31\ \text{A}$

(D)

Option D: $0.131\ \text{A}$

Q10. A uniform metallic wire of resistance $R$ is stretched uniformly to twice its original length while its volume remains constant. Neglecting any change in resistivity, the new resistance becomes

(A)

Option A: $2R$

(B)

Option B: $R/2$

(C)

Option C: $1.31\ \text{A}$

(D)

Option D: $R$

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