The time constant (τ) of an RC (resistor-capacitor) circuit is a measure of how quickly the circuit's voltage or current will change in response to a step input. It is defined as the product of the resistance (R) and the capacitance (C) in the circuit. The formula to calculate the time constant of an RC circuit is:
τ = R * C
τ = Time constant (in seconds)
R = Resistance (in ohms)
C = Capacitance (in farads)
When a step voltage is applied to an RC circuit, the voltage or current in the circuit will rise or decay over time towards its final value, and the time constant determines how quickly this process occurs. The larger the time constant, the slower the response of the circuit to the input change, and vice versa.