RC Circuits: Steady-State Behavior for AP Physics B & C

Practice problems for these concepts can be found at:

Circuits Practice Problems for AP Physics B & C

When you have both resistors and capacitors in a circuit, the circuit is called an "RC circuit."

On the Physics B exam, the only situation in which capacitors will show up in a circuit is when the circuit exhibits "steady-state behavior": this just means that the circuit has been connected for a while. In these cases, the only thing you'll generally need to worry about is how to deal with capacitors in series and in parallel.

When capacitors occur in series, you add them inversely. The charge stored on each capacitor in series must be the same.

For the circuit in Figure 21.10, the equivalent capacitance is C_eq = 1.5 μF.

When capacitors occur in parallel, you add them algebraically. The voltage across each capacitor in parallel must be the same.

The equivalent capacitance for the circuit in Figure 21.11 is 18 μF.

You should also know that the energy stored by a capacitor is

Once the circuit has been connected for a long time, capacitors stop current from flowing. To find the charge stored on or the voltage across a capacitor, just use the equation for capacitors, Q = CV.

For example, imagine that you hook up a 10-V battery to a 5 Ω resistor in series with an uncharged 1 F capacitor. (1 F capacitors are rarely used in actual electronics application—most capacitances are micro- or nanofarads—but they are commonly used for physics class demonstrations!) When the circuit is first hooked up, the capacitor is empty—it is ready and waiting for as much charge as can flow to it. Thus, initially, the circuit behaves as if the capacitor weren't there. In this case, then, the current through the resistor starts out at 10 V/5 Ω = 2 A.

But, after a long time, the capacitor blocks current. The resistor might as well not be there; we might as well just have a capacitor right across the battery. After a long time, the capacitor takes on the voltage of the battery, 10 V. (So the charge stored on the capacitor is Q = CV = 10 C.)

That's all you need for Physics B.

Physics C students need to know this … and more.

Practice problems for these concepts can be found at:

Circuits Practice Problems for AP Physics B & C