RC Time Constant Calculator

The RC time constant, represented as τ (tau), is a measure used in electrical engineering to quantify the time it takes for a capacitor, through a resistor, to charge to approximately 63.2% of the voltage supply or discharge to about 36.8% of its initial charge voltage.

Calculator

Enter

• Resistance R with units ohm (Ω)
• Capacitance C with units Farad (F)

Formula

τ = R*C

Where

• R is the resistance in ohm (Ω)
• C is the capacitance in Farad (F)
• τ is the time constant in seconds

Example Calculation

For a resistor value of 1 ohm and Capacitor value of 10 µF, the time constant is 10 µs.

Application

The significance of the RC time constant lies in its utility for predicting how quickly a circuit responds to a change in voltage.

For instance, in a charging capacitor scenario, the voltage across the capacitor at any time ( t ) can be calculated using the formula:

Vc = Vi (1-e-t/τ)

where,

• Vi = Input Voltage
• τ = time constant
• Vc = voltage at the capacitor at time t

time constant τ = RC, where R is resistance and C is capacitance.

Similarly, for a discharging capacitor, the voltage across it decreases over time following the exponential decay formula:

V = Vo*e−t/RC

The time constant time constant τ = RC, where R is resistance and C is capacitance. The time is typically specified as a multiple of the time constant.

t = RC*Loge(Vo/V)