RCcircuit

An RC circuit is an electrical circuit that contains a resistor and a capacitor. The two simplest configurations place the components in series with the input, and take the output either across the capacitor (a low-pass RC filter) or across the resistor (a high-pass RC filter).

With a step change in input, the capacitor charges or discharges with a characteristic time constant tau = RC. For a series RC with the output taken across the capacitor, the capacitor voltage follows Vc(t) = Vin (1 - e^{-t/RC}) for a 0-to-Vin step, and the current is i(t) = (Vin - Vc)/R = C dVc/dt. If the input is held at Vin and then released to zero, Vc(t) = Vc(0) e^{-t/RC} during discharge.

In the frequency domain, the low-pass transfer function is Vout/Vin = 1/(1 + jωRC), and the high-pass transfer function is Vout/Vin = jωRC/(1 + jωRC). The cutoff frequency is fc = 1/(2πRC).

Applications include filtering signals, timing and pulse shaping, and, in certain configurations, approximate integration or differentiation of signals. Practical RC circuits must account for non-idealities such as component tolerances, parasitic inductance and capacitance, leakage, and temperature effects, which can affect the actual response.