AP Physics 2 Kirchhoff's Rules and RC Circuits

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Complex circuit diagram with multiple loops and junctions.

Analyzing complex circuits requires more than just Ohm’s Law. We must use Conservation of Charge and Conservation of Energy to solve for unknown currents and voltages in compound systems.

1. Kirchhoff’s Rules (Topics 11.6 & 11.7)

These two rules are the foundation of all circuit analysis in AP Physics 2.

The Junction Rule (Conservation of Charge)

The total current entering a junction must equal the total current leaving it.

$\sum I_{in} = \sum I_{out}$

The Loop Rule (Conservation of Energy)

The sum of the potential differences (voltages) around any closed loop in a circuit must be zero.

$\sum \Delta V = 0$

2. Compound DC Circuits (Topic 11.5)

Most circuits on the exam are combinations of series and parallel components. To solve them, “collapse” the circuit into a single equivalent resistance ( $R_{eq}$ ).

$R_{series} = \sum R_i \quad \text{and} \quad \frac{1}{R_{parallel}} = \sum \frac{1}{R_i}$

Remember: Parallel resistors always result in a total resistance smaller than the smallest individual resistor.

3. Resistor-Capacitor (RC) Circuits (Topic 11.8)

In AP Physics 2, you primarily need to understand the steady-state behavior of RC circuits (time $t=0$ and $t \to \infty$ ).

At $t = 0$ (Uncharged): The capacitor acts like a wire (short circuit). Resistance is zero.
At $t \to \infty$ (Fully Charged): The capacitor acts like an open switch. No current flows through that branch.

AP Exam Tip: In RC circuits, pay close attention to whether the capacitor is in series or parallel with other resistors, as this changes the steady-state voltage across it.

4. Quick AP Practice

📚 Unit 11 Mastery Challenge

1. Two $10 \, \Omega$ resistors are connected in parallel. What is the equivalent resistance?

Check Answer

Using $1/R_{eq} = 1/10 + 1/10 = 2/10$ . Flipping it gives $R_{eq} = 10/2 = \mathbf{5 \, \Omega}$ .

2. A circuit branch contains a resistor and a capacitor. Long after the switch is closed, what is the current in that branch?