Alexander Fufaev

Formula: Resistor-Capacitor Circuit

Voltage-Time Graph - discharging capacitor

Time constant

Time constant is a characteristic quantity of a RC circuit, that is a resistor-capacitor circuit. The time constant indicates the time after which the voltage, charge or current at the capacitor has decreased or increased by the factor \( \frac{1}{\text e} \). \( \text e \) is the Euler number.

\( \frac{1}{\text e} \) correspond to 37% of the initial value. For example, if the capacitor was charged to \( 10 \, \mathrm{V} \) before discharge, this value decreases to \( 10 \cdot 0.37 = 3.7 \, \mathrm{V} \) after the time \( \tau \).


Electric capacitance of the capacitor. A capacitor with a large capacitance reaches 37% of the initial value later than a capacitor with a small capacitance.

Electrical Resistance

Resistor with electrical resistance \(R\) connected in parallel with the capacitor. The greater the resistance, the longer it takes for the initial value to fall or rise to 37%.