What is the formula for calculating the time constant of a circuit in terms of capacitance and resistance?

The time constant of a circuit, denoted as τ (tau), is a measure of how quickly a capacitor charges or discharges through a resistor in an RC (resistor-capacitor) circuit. The correct formula, τ = RC, directly relates the time constant to the resistance (R) and capacitance (C) values of the circuit.

When the circuit is connected to a voltage source, the time constant indicates the time it takes for the voltage across the capacitor to rise to approximately 63.2% of its final value after a step change in voltage, or for it to decay to about 36.8% of its initial voltage during discharge. This relationship shows how both resistance and capacitance together influence the rate of charging and discharging in the circuit—higher resistance or capacitance means a longer time constant, meaning it takes more time for the capacitor to charge or discharge.

In terms of units, resistance is measured in ohms (Ω) and capacitance in farads (F), making the product of RC yield a time constant measured in seconds, aligning with the concept's definition of time in electrical processes. This foundational principle is critical for anyone working with circuits, as it governs the timing characteristics of capacitive circuits