A capacitor is a passive component that stores energy in an electric field established between two conductive plates separated by a dielectric insulator. The amount of charge stored on the plates, \(Q\), is proportional to the capacitance \(C\) and the applied voltage \(V\), according to \(Q = CV\). Capacitance is measured in farads (F), defined as one coulomb per volt. The energy stored in a charged capacitor is \(E = \tfrac{1}{2}CV^2\). In a DC circuit, once a capacitor is fully charged, current ceases to flow, and the component behaves as an open circuit.
Capacitors combine in networks with rules opposite to those for resistors. In parallel, capacitances add directly: \(C_{total} = C_1 + C_2 + C_3 + \dots\). In series, the reciprocals add: \(1/C_{total} = 1/C_1 + 1/C_2 + 1/C_3 + \dots\). In AC analysis, a capacitor presents frequency-dependent impedance given by \(Z_C = 1/(j\omega C)\), where \(j\) is the imaginary unit and \(\omega\) is the angular frequency. This means capacitive impedance decreases as frequency rises, making capacitors useful for blocking DC while passing AC signals.
An inductor is a passive component, typically a coil of wire, that stores energy in a magnetic field. Its inductance is measured in henrys (H), defined as one volt-second per ampere. The energy stored in an inductor carrying current \(I\) is \(E = \tfrac{1}{2}LI^2\). Unlike a capacitor, an inductor in DC steady state behaves as a short circuit, passing DC current with no impedance once the current has stabilized. The impedance of an inductor in AC circuits is \(Z_L = j\omega L\), which increases with frequency. Inductors in series combine by direct addition, \(L_{total} = L_1 + L_2 + L_3 + \dots\) (assuming no mutual coupling), while in parallel they combine by the reciprocal rule, \(1/L_{total} = 1/L_1 + 1/L_2 + 1/L_3 + \dots\).