AP Physics 2 · Exam guide
AP Physics 2 Circuits Question: Series, Parallel, Current, and Power
A circuit question gives a battery and some resistors and asks for the current, the voltage across a resistor, or the power. The method is always the same: simplify to one equivalent resistance, find the total current, then work back out to each part. This guide follows one circuit.
The rules
| Arrangement | Resistance | Current and voltage |
|---|---|---|
| Series | \(R = R_1 + R_2 + \dots\) | The same current flows through each, and the voltages add. |
| Parallel | \(\dfrac{1}{R} = \dfrac{1}{R_1} + \dfrac{1}{R_2} + \dots\) | The same voltage across each, and the currents add. |
A worked example
A 12 V battery is connected to a 4 \(\Omega\) resistor in series with two resistors in parallel, 6 \(\Omega\) and 3 \(\Omega\). Find (a) the total current, (b) the current through the 6 \(\Omega\) resistor, and (c) the total power supplied.
(a) The parallel pair: \(\dfrac{1}{R_p} = \dfrac{1}{6} + \dfrac{1}{3} = \dfrac{1}{2}\), so \(R_p = 2\ \Omega\). The total is \(4 + 2 = 6\ \Omega\), and \(I = \dfrac{12}{6} = 2.0\) A.
(b) The 2.0 A flows through the 4 \(\Omega\) resistor, which drops 8 V, so the parallel pair has 4 V across it. The current through the 6 \(\Omega\) resistor is \(\dfrac{4}{6} = 0.67\) A. The 3 \(\Omega\) resistor carries \(\dfrac{4}{3} = 1.33\) A, and the two add to 2.0 A.
(c) \(P = IV = (2.0)(12) = 24\) W. As a check, the power in the resistors is \(I^2R\): 16 W in the 4 \(\Omega\) resistor, and \(4 \times 2.0 = 8\) W in the parallel pair, which also gives 24 W.
It uses the battery voltage across a resistor that is not directly connected to the battery.
It finds the voltage across that resistor before using Ohm's law.
Checks that catch errors
- Parallel resistance is smaller than the smallest branch.
- The branch currents add up to the total current.
- The voltage drops around the loop add up to the battery voltage.
- The power supplied equals the power dissipated.
Common mistakes
- Adding parallel resistors as if they were in series.
- Using the battery voltage across every resistor.
- Forgetting to take the reciprocal at the end of a parallel calculation.
- Leaving out units, or mixing watts and joules.
Frequently asked questions
What if the battery has internal resistance?
Treat it as another resistor in series with the battery.
What happens to the total current if I add a resistor in parallel?
It increases, because the total resistance decreases.
How do I find the power in one resistor?
Use I squared times R, V squared over R, or I times V, with the values for that resistor.
Where can I find the official scoring rules?
Exam formats change a little from year to year, so check the current course and exam description on the College Board site before test day.
Keep practicing
Every lesson in the AP Physics courses ends with practice problems and an Exam focus box that shows how the topic is tested, and every unit has a review with worked answers. These free lessons also build the skills the free-response section tests:
See the AP Physics 2 course Free lessons and lesson list
More AP Physics 2 guides (6)
Start here
Free-response and writing
- AP Physics 2 Experimental Design Explained: Planning an Experiment and Analyzing the Data
- AP Physics 2 Thermodynamics FRQ Explained: PV Diagrams and the First Law
- AP Physics 2 Optics Question: The Lens Equation and Image Types
- AP Physics 2 Photoelectric Effect: Photon Energy, Work Function, and Stopping Potential
Multiple choice
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