Circuits · AP Physics 2 · 6 min
A capacitor is not simply a wire or a break; its circuit role depends on the time after the switch changes.
01 The trap
Wrong path
Students use one capacitor shortcut for every moment in an RC circuit.
Why it feels right
RC circuits often get taught with final formulas, so the physical before/after states get blurred.
02 Correct model
An uncharged capacitor initially behaves like a short in a DC charging circuit. After a long time, a fully charged capacitor behaves like an open branch for steady DC.
03 Mini-example
Prompt
A resistor and uncharged capacitor are in series with a battery. What is the initial current right after the switch closes?
Common wrong answer
Zero, because the capacitor blocks current.
Correct reasoning
Initially the capacitor has no voltage, so the initial current is V/R.
Diagnostic cue
Words like 'immediately after' and 'after a long time' are circuit-state commands, not decoration.
04 Guided practice
Warm-up isolates the principle. Bridge changes the context. Contest-style requires a complete setup on less familiar geometry.
An uncharged capacitor and resistor are in series with a battery. Immediately after the switch closes, what is the capacitor's voltage?
An uncharged capacitor initially has zero voltage across it.
The capacitor voltage is initially 0 V. It begins uncharged, so it initially behaves like a wire for the purpose of the series current.
Trap: Using the long-time open-circuit behavior at t = 0.
A 12 V battery, 4.0 kΩ resistor, and capacitor are in series. After a very long time, what is the current?
After a long time, the ideal capacitor no longer allows steady current.
The long-time current is 0 A. The capacitor is fully charged and behaves as an open circuit in steady DC.
Trap: Using I = V/R = 3.0 mA after the capacitor is already fully charged.
For a charging RC circuit, should the current graph start high and decay toward zero, start at zero and rise, or stay constant?
Initially the uncharged capacitor acts like a wire; finally it acts like an open circuit.
The current starts at its maximum value V/R and decays toward zero as the capacitor charges and its voltage increases.
Trap: Treating the capacitor like a battery that slowly creates current.
A 22 kΩ resistor is in series with a 47 μF capacitor. What is the circuit's time constant?
22 kΩ = 22,000 Ω and 47 μF = 47 × 10⁻⁶ F.
τ = RC = (22,000)(47 × 10⁻⁶) = 1.034 s, about 1.03 s.
Trap: Treating kilo and micro as if they cancel exactly.