Quiz: Electric Current and Circuits — 14 questions

1. Regarding electric charge and current, which statements are correct?

A. A proton and a sodium ion each carry charge $+e$.

B. A silicon ion $\mathrm{Si}^{2-}$ carries charge $+2e$.

C. Conventional current follows the motion of negative charges.

D. Electric charge is quantized according to $q=Ze$.

E. Electric current measures charge flow through a section over time.

Answer: (A), (D), (E)

Explanation

Electric charge is quantized as $q=Ze$, while current measures charge flow per unit time. A proton and a sodium ion each carry $+e$, whereas $\mathrm{Si}^{2-}$ carries $-2e$; conventional current follows positive-charge motion and opposes negative-charge motion.

2. Concerning the definitions and direction of electric current, select the correct statements:

A. Electric current is given by $I=\frac{dq}{dt}$.

B. Conventional current is directed opposite to positive-charge motion.

C. Conventional current follows the motion of negative charges.

D. Electric charge and electric current represent identical physical quantities.

E. A silicon ion $\mathrm{Si}^{2-}$ carries charge $-2e$.

Answer: (A), (E)

Explanation

Current is defined by $I=\frac{dq}{dt}$, so it is distinct from the charge itself. Conventional current follows positive-charge motion and opposes negative-charge motion; a silicon ion with charge $-2e$ is negative.

3. The characteristics of electric charge and conventional current include:

A. Conventional current follows positive-charge motion.

B. A proton carries charge $-e$.

C. Quantized electric charge can be written as $q=Ze$.

D. Conventional current follows negative-charge motion.

E. A semiconductor hole carries charge $+e$.

Answer: (A), (C), (E)

Explanation

The relation $q=Ze$ describes quantized charge. A hole has charge $+e$, a proton has $+e$, and conventional current is defined in the direction of positive-charge motion, opposite to negative-charge motion.

4. Regarding charge flow in a conductor, which statements are correct?

A. The drift speed is $v=\frac{I}{enS}$.

B. For a circular conductor, $S=\pi(D/2)^2$.

C. Current is determined by carrier charge without reference to speed or section.

D. The current magnitude is $I=envS$.

E. The drift speed is approximately $10^6\ \mathrm{m\,s^{-1}}$.

Answer: (A), (B), (D)

Explanation

For carriers of charge $e$, the current magnitude is $I=envS$, and solving for drift speed gives $v=\frac{I}{enS}$. The cross-sectional area of a circular conductor is $S=\pi(D/2)^2$; drift speed is about $10^{-5}\ \mathrm{m\,s^{-1}}$, far below thermal speed.

5. Concerning carrier speed and current in a conductor, choose the correct statements:

A. Increasing the carrier speed increases the current when other factors remain fixed.

B. The drift speed is calculated as $v=\frac{enS}{I}$.

C. The propagation speed is approximately $3\times10^8\ \mathrm{m\,s^{-1}}$.

D. The drift speed is approximately $10^{-5}\ \mathrm{m\,s^{-1}}$.

E. The thermal speed is approximately $10^6\ \mathrm{m\,s^{-1}}$.

Answer: (A), (C), (D), (E)

Explanation

The formula $v=\frac{I}{enS}$ gives the carrier drift speed, and the current relation is $I=envS$. Drift speed is about $10^{-5}\ \mathrm{m\,s^{-1}}$, thermal speed about $10^6\ \mathrm{m\,s^{-1}}$, and propagation speed about $3\times10^8\ \mathrm{m\,s^{-1}}$.

6. A circular conductor has diameter $D$ and carries charge carriers of density $n$. Which statements are correct?

A. The current magnitude is $I=envS$.

B. The current magnitude is independent of the conductor’s cross-sectional area.

C. The drift speed is approximately $10^6\ \mathrm{m\,s^{-1}}$.

D. Its cross-sectional area is $S=\pi(D/2)^2$.

E. The propagation speed is approximately $10^{-5}\ \mathrm{m\,s^{-1}}$.

Answer: (A), (D)

Explanation

For a circular conductor, $S=\pi(D/2)^2$, and current is $I=envS$. The drift speed is approximately $10^{-5}\ \mathrm{m\,s^{-1}}$, not the much larger thermal speed or propagation speed.

7. Concerning the quasi-static approximation for circuits, select the correct statements:

A. When $T=1/f$, the condition becomes $L\ll f/c$.

B. The approximation treats electrical changes as effectively instantaneous throughout the circuit.

C. Its validity requires $\tau\ll T$.

D. At 50 Hz, the scale $c/f$ is approximately $6\times10^6\ \mathrm{m}$.

E. For a circuit of length $L$, propagation time is $\tau=L/c$.

Answer: (B), (C), (D), (E)

Explanation

The quasi-static approximation applies when propagation time is negligible compared with variation time, expressed as $\tau\ll T$. Since $\tau=L/c$ and $T=1/f$, this becomes $L\ll c/f$; at 50 Hz, $c/f=6\times10^6\ \mathrm{m}$.

8. A circuit operates at frequency $f$ with signal speed $c$. Which statements correctly describe the quasi-static condition?

A. Using $T=1/f$ gives the condition $L\ll c/f$.

B. The maximum characteristic length decreases as frequency decreases.

C. The maximum characteristic length decreases as frequency increases.

D. The approximation requires propagation and variation times to be comparable.

E. The propagation time across length $L$ is $\tau=L/c$.

Answer: (A), (C), (E)

Explanation

The propagation time is $\tau=L/c$, and the quasi-static condition is $\tau\ll T$. With $T=1/f$, this gives $L\ll c/f$; increasing frequency reduces the maximum characteristic length.

9. At 50 Hz, which statements correctly characterize the quasi-static approximation?

A. A circuit much shorter than this scale can generally use the approximation.

B. The condition for a circuit of length $L$ is $L\ll f/c$.

C. The reference length scale $c/f$ is approximately $6000\ \mathrm{km}$.

D. The approximation is generally used below about $600\ \mathrm{km}$.

E. The approximation requires propagation time to be comparable with variation time.

Answer: (A), (C), (D)

Explanation

At 50 Hz, $c/f=6\times10^6\ \mathrm{m}=6000\ \mathrm{km}$, so circuits much shorter than this scale generally satisfy the approximation. The approximation requires $\tau\ll T$, not comparable times, and the condition is $L\ll c/f$.

10. Regarding circuit topology vocabulary, which statements are correct?

A. Two dipoles in parallel carry the same current.

B. A node is a point where connected circuit wires meet.

C. Two dipoles in series are subjected to the same voltage.

D. A mesh is a closed circuit part that avoids revisiting any node.

E. A branch is a circuit portion located between two nodes.

Answer: (B), (D), (E)

Explanation

A node is where connected wires meet, whereas a branch is the circuit portion between two nodes. A mesh is a closed circuit part that does not revisit a node, and series or parallel classification depends on shared current or voltage respectively.

11. Which statements correctly distinguish circuit topology terms?

A. Two series dipoles carry the same current.

B. A mesh forms a closed part without repeating a node.

C. A node is the circuit portion extending between two connection points.

D. A branch is a portion of circuit between two nodes.

E. Two parallel dipoles carry the same current.

Answer: (A), (B), (D)

Explanation

A mesh is defined as a closed part of a circuit that does not pass through the same node more than once. A branch lies between two nodes, while series elements share current and parallel elements share voltage.

12. Concerning series and parallel dipoles, select the correct statements:

A. Series dipoles carry an identical current through each dipole.

B. Parallel dipoles are subjected to an identical voltage.

C. Parallel dipoles carry an identical current through each dipole.

D. A mesh may pass through one node repeatedly while remaining closed.

E. Series dipoles are subjected to an identical voltage.

Answer: (A), (B)

Explanation

Series dipoles carry the same current, while parallel dipoles experience the same voltage. A node is a connection point, a branch lies between nodes, and a mesh does not revisit a node.

13. Regarding Kirchhoff’s node law, which statements are correct?

A. The law expresses conservation of electric charge.

B. The law applies in the quasi-static approximation.

C. Incoming current equals outgoing current at a node.

D. The relation can be written as an algebraic zero sum after choosing current signs.

E. The law concerns voltage sums around a mesh.

Answer: (A), (B), (C), (D)

Explanation

The node law states that incoming current equals outgoing current in the quasi-static approximation, expressing electric-charge conservation. It concerns currents rather than voltage sums, and an algebraic zero form requires a chosen sign convention.

14. For Kirchhoff’s mesh law, which propositions are correct?

A. Individual voltages along a path generally have equal values.

B. The mesh equation equates total incoming and outgoing currents.

C. A chosen traversal direction determines the voltage signs in the mesh sum.

D. The stated orientation gives $u_3=u_1+u_2+u_4$.

E. Voltage differences along a path satisfy $U_{AC}=U_{AB}+U_{BC}$.

Answer: (C), (D), (E)

Explanation

Around a mesh, the algebraic sum of voltages is zero, and voltage differences add along a path according to $U_{AC}=U_{AB}+U_{BC}$. The stated orientation also gives $u_3=u_1+u_2+u_4$, whereas node laws concern currents.