resistorcapacitor

Resistor-capacitor, commonly abbreviated RC, denotes a network that combines a resistor and a capacitor. In typical circuits the two components are connected in series or in parallel. RC networks are widely used to shape temporal or frequency characteristics of signals. The behavior of an RC network is governed by the time constant τ = R C, which sets the rate at which the capacitor charges or discharges.

For a series RC with a step input, the capacitor voltage during charging is Vc(t) = Vin (1 − e^(−t/RC)) and the current is i(t) = (Vin/R) e^(−t/RC). When the input is removed or grounded, the capacitor discharges according to Vc(t) = V0 e^(−t/RC).

RC networks form basic filters. A resistor and capacitor in series with the output taken across the capacitor yields a low-pass filter with cutoff frequency fc = 1/(2π R C). If the output is taken across the resistor, it becomes a high-pass filter with the same cutoff. The transfer functions are H(s) = 1/(1 + s R C) for the low-pass and H(s) = s R C /(1 + s R C) for the high-pass, in Laplace form.

Common applications include timing circuits, smoothing and energy storage, signal conditioning, and as building blocks in op-amp integrators and differentiators. Practical RC designs must account for component tolerances, leakage currents, equivalent series resistance (ESR) of capacitors, and temperature coefficients.