Time constant

Definition

The time constant ($\tau$) of an RC circuit is the time it takes for the voltage across the capacitor to either charge or discharge to approximately 63% of its full value. It is calculated as the product of resistance (R) and capacitance (C): $\tau = RC$.

5 Must Know Facts For Your Next Test

1. The time constant determines how quickly an RC circuit responds to changes in voltage.
2. After five time constants, a capacitor in an RC circuit is considered to be fully charged or discharged.
3. In an RC charging circuit, the voltage across the capacitor as a function of time is given by $V(t) = V_0(1 - e^{-t/\tau})$.
4. In an RC discharging circuit, the voltage across the capacitor as a function of time is given by $V(t) = V_0 e^{-t/\tau}$.
5. $\tau$ has units of seconds, derived from multiplying ohms (resistance) by farads (capacitance).

Review Questions

• How do you calculate the time constant ($\tau$) in an RC circuit?
• What percentage of its final value does a capacitor reach after one time constant during charging?
• How many time constants are generally considered enough for a capacitor to be fully charged or discharged?

Related terms

Capacitance:

The ability of a system to store charge per unit voltage, measured in farads (F).

Resistance:

A measure of opposition to current flow in an electrical circuit, measured in ohms ($\Omega$).

$e^{-t/\tau}$: The exponential factor that describes how voltages change over time in both charging and discharging processes in RC circuits.