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AP Physics 2: Algebra-Based Practice Quiz: Kirchhoff's Loop Rule

Written by AP Content Team, Verified for 2026 AP Exams, Last updated: May 2026

Test your understanding with short quizzes. This quiz has 10 questions to check your progress.

Question 1 of 10

Which of the following statements is the correct definition of Kirchhoff's loop rule?

All Questions (10)

Which of the following statements is the correct definition of Kirchhoff's loop rule?

A) The sum of all currents entering a junction must equal the sum of all currents leaving the junction.

B) The total resistance in a series circuit is the sum of the individual resistances.

C) The sum of potential differences across all circuit elements in a single closed loop must equal zero.

D) The electric potential at all points within a closed circuit must be constant.

Correct Answer: C

Kirchhoff's loop rule, expressed as ΣΔV=0, states that the algebraic sum of the changes in electric potential around any closed circuit path (loop) is zero. Option A describes Kirchhoff's junction rule.

Kirchhoff's loop rule is a direct consequence of which fundamental physical principle?

A) Conservation of charge

B) Conservation of energy

C) Conservation of momentum

D) Newton's second law

Correct Answer: B

The loop rule is an application of the conservation of energy. As a charge moves around a closed loop and returns to its starting point, its net change in potential energy must be zero. Since electric potential is potential energy per unit charge, the net change in potential must also be zero.

A simple circuit contains an ideal battery with voltage V and two resistors, R1 and R2, connected in series. Which equation correctly represents an application of Kirchhoff's loop rule for a complete loop starting at the negative terminal and moving in the direction of the current?

A) V + I*R1 + I*R2 = 0

B) V - I*R1 - I*R2 = 0

C) V - I*R1 + I*R2 = 0

D) I*R1 + I*R2 = 0

Correct Answer: B

Starting at the negative terminal and moving through the battery results in a potential gain of +V. Moving through each resistor in the direction of the current results in a potential drop, represented as -I*R. Summing these potential differences for the entire loop gives V - I*R1 - I*R2 = 0.

If a charge carrier completes one full trip around a closed circuit loop, what can be concluded based on Kirchhoff's loop rule?

A) The net work done on the charge carrier by the electric field is zero.

B) The charge carrier's velocity returns to its initial value.

C) The electric potential at its starting point is the same as when it returns.

D) The total resistance encountered by the charge carrier is zero.

Correct Answer: C

The loop rule (ΣΔV=0) means that the net change in potential around the loop is zero. Therefore, the potential at any point must be the same each time a charge carrier passes it, meaning the potential at the end of a complete loop is identical to the potential at the start.

A graph of electric potential versus position is created for a single-loop circuit. The graph shows a sharp, vertical increase in potential, followed by a region of gradual, linear decrease. The sharp increase most likely corresponds to the charge passing through which circuit element?

A) A resistor

B) A connecting wire with negligible resistance

C) An ideal voltage source (battery)

D) A switch that has just been closed

Correct Answer: C

An ideal voltage source, like a battery, provides a nearly instantaneous increase in electric potential as a charge moves from its negative to its positive terminal. A resistor causes a potential drop (decrease), and an ideal wire would show no change in potential (a flat line).

In a closed loop, an ideal 9 V battery is connected to two series resistors. The potential difference across the first resistor is measured to be 6 V. According to Kirchhoff's loop rule, what must be the potential difference across the second resistor?

A) 15 V

B) 9 V

C) 6 V

D) 3 V

Correct Answer: D

By Kirchhoff's loop rule, the sum of potential differences is zero. The battery provides a gain of +9 V. The first resistor causes a drop of -6 V. To make the sum zero, the second resistor must cause a drop of -3 V. The equation is: +9V - 6V - ΔV₂ = 0, which solves to ΔV₂ = 3V.

The equation ΣΔV=0 is the mathematical representation of Kirchhoff's loop rule. What does the term ΔV represent?

A) The total voltage supplied by the battery.

B) The change in current across a circuit element.

C) The potential difference across a single circuit element.

D) The total energy dissipated by the circuit.

Correct Answer: C

In the context of the loop rule, ΔV represents the change in electric potential, or potential difference, experienced when moving across a single circuit element (like a battery, resistor, or capacitor). The rule states that the sum (Σ) of all these individual potential differences in a loop is zero.

A student analyzes a graph of electric potential as a function of position for a closed loop. They observe that the potential at the end of the graph is higher than the potential at the beginning. What is the most likely error in the student's analysis or the graph's representation?

A) The circuit contains more than one battery.

B) The graph does not represent a complete closed loop.

C) The resistors in the circuit have very high resistance.

D) The current in the circuit is flowing in the reverse direction.

Correct Answer: B

Kirchhoff's loop rule, a consequence of energy conservation, dictates that the potential must return to its starting value after a complete loop (ΣΔV=0). If the final potential is different from the initial potential, the path analyzed did not constitute a complete, closed loop.

When describing a circuit by applying Kirchhoff's loop rule, the potential difference across a resistor is considered a 'potential drop' when the loop is traversed in the direction of the current. This is because...

A) resistors create and store electric energy.

B) charge carriers gain kinetic energy as they pass through a resistor.

C) electric potential energy is converted into thermal energy in the resistor.

D) the resistance of the circuit is decreasing at that point.

Correct Answer: C

The loop rule is based on conservation of energy. As current flows through a resistor, collisions within the material convert the electric potential energy of the charge carriers into thermal energy (heat). This loss of electric potential energy corresponds to a drop in electric potential.

Which of the following scenarios in a circuit is a direct violation of Kirchhoff's loop rule?

A) A circuit where the current is zero.

B) A charge completing a loop and returning to its starting point with less potential energy than it started with.

C) A circuit loop where the sum of potential gains from batteries equals the sum of potential drops across resistors.

D) A charge completing a loop and returning to its starting point with the same electric potential it started with.

Correct Answer: B

Kirchhoff's loop rule is a statement of conservation of energy. A charge returning to its starting point must have the same potential energy and thus the same electric potential. If it returned with less potential energy, energy would not be conserved, which violates the fundamental principle behind the rule. Options C and D are restatements of the rule being followed.