3.8 Resistor-Capacitor (RC) Circuits

Charging an RC Circuit

When a capacitor charges through a resistor, current and voltage change exponentially over time rather than instantly. Initially the capacitor is uncharged (acts like a wire), so current is maximum. As charge builds, capacitor voltage rises toward the source voltage while current decays toward zero. The time constant τ = RC describes how quickly this happens.

Discharging an RC Circuit

When a charged capacitor discharges through a resistor, both voltage and current decay exponentially from their initial values toward zero. Larger resistance or capacitance means slower charging/discharging (larger τ = RC). After about 5τ, the capacitor is considered fully charged or discharged.

Qualitative Graphs and Behavior

On charging graphs, capacitor voltage/charge increases with decreasing slope (concave down, approaching max asymptotically); current decreases exponentially from a max value. On discharging graphs, voltage, charge, and current all decrease exponentially from their initial values toward zero. AP Physics 2 emphasizes qualitative and graphical understanding rather than exponential equations.

Key terms

Time constant (τ)

τ = RC; determines how quickly a capacitor charges or discharges in an RC circuit.

Capacitor behavior at t = 0 (charging)

Acts like a wire (no resistance); current is at its maximum value.

Capacitor behavior at t = ∞ (charging)

Acts like an open switch (fully charged); current approaches zero.

Charging graph shapes

Capacitor voltage/charge rises with decreasing slope (concave down) toward max; current falls exponentially toward zero.

Discharging graph shapes

Voltage, charge, and current all decay exponentially from initial values toward zero.

Try an AP-style question

What is the time constant of an RC circuit with R = 1,000 Ω and C = 1.0 mF?

1. 1.0 s
2. 1,000 s
3. 0.001 s
4. 10 s