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AP Physics C: Electricity and Magnetism Practice Quiz: Circuits with Capacitors and Inductors (LC Circuits)

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

In an ideal LC circuit, which physical principle is fundamental to determining the maximum current in the inductor, given the initial maximum charge on the capacitor?

All Questions (10)

In an ideal LC circuit, which physical principle is fundamental to determining the maximum current in the inductor, given the initial maximum charge on the capacitor?

A) Ohm's Law

B) Conservation of Energy

C) Kirchhoff's Junction Rule

D) Gauss's Law

Correct Answer: B

According to the provided content, in LC circuits, the maximum current in the inductor can be determined using conservation of energy. The initial potential energy stored in the capacitor's electric field (when current is zero) is converted into magnetic potential energy in the inductor (when charge is zero and current is maximum).

An LC circuit oscillates with an angular frequency ω. If the inductance L is kept constant but the capacitance C is quadrupled, what is the new angular frequency of the circuit?

A) 4ω

B) 2ω

C) ω/2

D) ω/4

Correct Answer: C

The angular frequency of an LC circuit is given by the equation ω = 1/√(LC). If the capacitance C is replaced by 4C, the new angular frequency ω' will be ω' = 1/√(L(4C)) = 1/(2√(LC)) = ω/2.

The charge q on a capacitor in an LC circuit as a function of time t is described by the differential equation d²q/dt² = - (1/LC)q. This equation is the defining characteristic of what type of physical behavior?

A) Exponential decay

B) Uniform linear motion

C) Simple harmonic motion

D) Damped oscillation

Correct Answer: C

The provided content explicitly states that the time dependence of the charge stored in the capacitor can be modeled as simple harmonic motion, and it provides the corresponding differential equation. The form d²x/dt² = - (constant) * x is the mathematical definition of simple harmonic motion.

In an oscillating LC circuit, at the instant the current in the inductor is at its maximum value, what is the amount of charge stored on the capacitor plates?

A) The maximum possible charge, Q_max

B) Half the maximum charge, Q_max/2

C) Zero

D) An indeterminate value between zero and Q_max

Correct Answer: C

Based on the principle of conservation of energy, the total energy in the circuit is constant. When the current is maximum, the energy stored in the inductor's magnetic field is maximum. For the total energy to remain constant, the energy stored in the capacitor's electric field must be zero. Since capacitor energy is U_C = q²/(2C), the charge q must be zero.

An LC circuit is designed to have a specific angular frequency ω. If an engineer needs to build a new circuit with double the original angular frequency (2ω), which of the following modifications to the inductance L and capacitance C would achieve this?

A) Double the inductance and double the capacitance.

B) Halve the inductance and halve the capacitance.

C) Double the inductance and halve the capacitance.

D) Quadruple the inductance and keep the capacitance the same.

Correct Answer: B

The angular frequency is ω = 1/√(LC). The new frequency is ω' = 2ω. We need to find L' and C' such that 1/√(L'C') = 2 * (1/√(LC)). Let's test the options. For option B, L' = L/2 and C' = C/2. Then ω' = 1/√((L/2)(C/2)) = 1/√(LC/4) = 2/√(LC) = 2ω. This is the correct modification.

Which of the following circuit elements are essential for creating an LC circuit where the charge on a component oscillates in simple harmonic motion?

A) A resistor and a capacitor

B) A battery and an inductor

C) A capacitor and an inductor

D) A resistor and a battery

Correct Answer: C

The provided content describes the physical and electrical properties of a circuit containing a combination of capacitors and a single inductor. This combination, an LC circuit, is the one in which charge exhibits simple harmonic motion.

The differential equation for an LC circuit is d²q/dt² = - (1/LC)q. By comparing this to the standard form of the simple harmonic motion equation, d²x/dt² = -ω²x, what does the term 1/LC represent?

A) The period of oscillation squared, T²

B) The angular frequency, ω

C) The square of the angular frequency, ω²

D) The maximum charge, Q_max

Correct Answer: C

By direct comparison of the two equations, the charge q is analogous to the position x. The term multiplying the negative q must be analogous to the term multiplying the negative x. Therefore, 1/LC is equivalent to ω², the square of the angular frequency. This leads directly to the derived equation ω = 1/√(LC).

In an ideal LC circuit, at the moment the capacitor holds its maximum charge, where is the energy of the circuit stored?

A) Entirely in the magnetic field of the inductor.

B) Entirely in the electric field of the capacitor.

C) Equally shared between the inductor and the capacitor.

D) The circuit contains no energy at this instant.

Correct Answer: B

When the capacitor has maximum charge (q = Q_max), the rate of change of charge (current, i = dq/dt) is momentarily zero. According to the principle of energy conservation, the total energy is the sum of the capacitor's energy (q²/(2C)) and the inductor's energy (Li²/2). With i=0, all the energy is stored in the capacitor.

The angular frequency of an LC circuit is determined by ω = 1/√(LC). What does this relationship imply about the period of oscillation?

A) The period is directly proportional to both L and C.

B) The period is inversely proportional to the square root of the product of L and C.

C) The period is directly proportional to the square root of the product of L and C.

D) The period is independent of L and C.

Correct Answer: C

The period T is related to the angular frequency ω by T = 2π/ω. Substituting the expression for ω from the provided content, we get T = 2π / (1/√(LC)) = 2π√(LC). Therefore, the period is directly proportional to the square root of the product of L and C.

An LC circuit has an initial maximum charge Q_max on the capacitor. Using the principle of energy conservation, what is the expression for the maximum current, I_max, in the inductor?

A) I_max = Q_max / (LC)

B) I_max = Q_max * √(L/C)

C) I_max = Q_max * √(C/L)

D) I_max = Q_max / √(LC)

Correct Answer: D

By conservation of energy, the maximum energy stored in the capacitor must equal the maximum energy stored in the inductor. So, U_C_max = U_L_max, which is (Q_max)²/(2C) = L(I_max)²/2. Solving for I_max: (Q_max)²/C = L(I_max)², so (I_max)² = (Q_max)²/(LC). Taking the square root gives I_max = Q_max / √(LC).