AP Physics C: Electricity and Magnetism, AP exams

Unit 11: Electric Circuits

Unit 11 covers steady-state and time-dependent direct-current circuits. Resistors in series and parallel and Kirchhoff's rules handle the steady case, while RC circuits introduce exponential charging and discharging with a characteristic time constant. Sketching and interpreting those exponential curves is a frequent exam task.

Position: 4 of 6 units
Topics covered: 5 topics in this guide

What is covered

Topics inside this unit.

These topics describe the scope students most often review for this part of AP Physics C: Electricity and Magnetism. Treat them as a study checklist rather than an exhaustive list of what a single exam form can sample.

Current, resistivity, and resistance: Current as charge flow rate, and how geometry and material set resistance.
Series and parallel combinations: Equivalent resistance and capacitance, and how current and potential difference distribute.
Kirchhoff's rules: Junction and loop rules as statements of charge and energy conservation, applied to multiloop circuits.
Power and internal resistance: Energy dissipation in resistors, terminal voltage, and the effect of a battery's internal resistance.
RC circuits: Exponential charging and discharging, the time constant, and the initial and final behavior of the circuit.

Study tips

How to practice Electric Circuits.

Section-specific guidance that follows from how this material is usually tested.

Learn the two limiting behaviors of a capacitor in a circuit: uncharged behaves like a wire, fully charged behaves like a break.
Sketch charge and current versus time for both charging and discharging and label the time constant on each.
Redraw multiloop circuits before applying Kirchhoff's rules, and assign loop directions before writing equations.

Where this fits

Unit 11: Electric Circuits is 4 of 6 units in the AP Physics C: Electricity and Magnetism guide. Use the full guide to balance it against everything else you have to review.

Back to the AP Physics C: Electricity and Magnetism guide Official exam information

Sample Electric Circuits questions

Practice questions, not yet expert-reviewed

Original practice questions written to the published framework for this section. No expert has reviewed them, and they are not taken from any official exam. Try each one before you open the answer.

Question 1Foundational
A 2.0 x 10^-6 F capacitor is connected in series with a 5.0 x 10^5 ohm resistor and a battery. What is the time constant of this RC circuit?
1. A0.10 s
2. B1.0 s
3. C2.5 s
4. D10 s
Show answer
Answer: B. 1.0 s
The time constant is the product RC = (5.0 x 10^5)(2.0 x 10^-6) = 1.0 s. The 10 s choice slips a power of ten in the capacitance, and dividing the resistance by the capacitance instead of multiplying does not even yield units of time.
Key insight: One time constant is the time for a charging capacitor to reach about 63 percent of its final charge.
Question 2Foundational
A capacitor, a resistor of resistance R, and a battery of emf V are connected in series. A very long time after the switch is closed, what is the current through the resistor?
1. AZero
2. BV/R
3. CV/(2R)
4. DIt increases without limit
Show answer
Answer: A. Zero
As the capacitor charges, its potential difference rises until it opposes the entire battery emf, leaving no net driving potential and therefore no current. The V/R choice is the initial current at the instant the switch closes, when the uncharged capacitor behaves like a plain wire.
Key insight: In a DC circuit an uncharged capacitor acts like a wire and a fully charged one acts like a break.
Question 3Intermediate
A battery of emf 12 V and internal resistance 0.50 ohms is connected to an external 5.5 ohm resistor. What is the terminal voltage of the battery?
1. A1.0 V
2. B10 V
3. C11 V
4. D12 V
Show answer
Answer: C. 11 V
The current is 12 V/(0.50 + 5.5) ohms = 2.0 A, so the internal resistance drops (2.0 A)(0.50 ohms) = 1.0 V and the terminal voltage is 12 - 1.0 = 11 V. The 12 V choice would be the terminal voltage only with no current drawn.
Key insight: Terminal voltage falls below the emf whenever current flows, and the gap grows with the current drawn.
Question 4Intermediate
A 4.0 ohm resistor and a 12 ohm resistor are connected in parallel, and that combination is in series with a 3.0 ohm resistor across an ideal 12 V battery. What is the current delivered by the battery?
1. A0.63 A
2. B1.3 A
3. C2.0 A
4. D4.0 A
Show answer
Answer: C. 2.0 A
The parallel pair is (4.0)(12)/(16) = 3.0 ohms, so the total resistance is 3.0 + 3.0 = 6.0 ohms and the current is 12/6.0 = 2.0 A. The 0.63 A choice adds all three resistances in series, which overstates the resistance of the parallel branch.
Key insight: Reduce a circuit to a single equivalent resistance in stages, innermost combination first.
Question 5Advanced
An initially uncharged capacitor is charged through a resistor by a battery in a series RC circuit. After a time equal to two time constants, what percentage of the final charge is on the capacitor?
1. AAbout 14%
2. BAbout 63%
3. CAbout 86%
4. DAbout 95%
Show answer
Answer: C. About 86%
Charging follows q(t) = Q(1 - e^(-t/RC)), so at t = 2RC the fraction is 1 - e^-2 = 0.865. The 63% choice is the value after one time constant, and 14% is the fraction still missing after two.
Key insight: Exponential approach never quite finishes, but each additional time constant removes another factor of e from the gap.

Continue through AP Physics C: Electricity and Magnetism

Practice Electric Circuits deliberately.

Create your Arcade Academy workspace to turn this topic list into spaced-repetition reviews, linked notes, and progress you can act on.

Create your account

Unit 11: Electric Circuits