AP Physics C: Electricity and Magnetism / Unit 11: Electric Circuits
11.8 Resistor-Capacitor (RC) Circuits
Notes
Charging: $q(t)=C\varepsilon\left(1-e^{-t/RC}\right)$, $\displaystyle I(t)=\frac{\varepsilon}{R}e^{-t/RC}$. Discharging: $q(t)=Q_0e^{-t/RC}$.
- Time constant $\tau=RC$: after one $\tau$, charging reaches about 63%.
Practice
After one time constant while charging, $q$ is about:
$1-e^{-1}$.
The initial current when charging through $R$ from $\varepsilon$:
Capacitor acts like a wire.
The differential equation for discharging is:
Loop rule: $\displaystyle \frac{q}{C}+IR=0$.
Ready for more? Take the Unit 11 test.