Capacitors

A capacitor stores charge and energy: $C = Q/V$, with $U = \tfrac{1}{2}CV^2$. Parallel-plate capacitance is $C = \kappa\epsilon_0 A/d$, and a dielectric raises it. Capacitors add oppositely to resistors: directly in parallel, reciprocally in series. In RC behavior, an uncharged capacitor initially acts like a wire and, once charged, like a break in the circuit.

Key Takeaways

• Series: same current, voltages divide. Parallel: same voltage, currents divide.
• Adding a parallel resistor always lowers total resistance.
• Use whichever form of $P$ matches the known quantities.
• Capacitor combination rules are the reverse of resistor rules.