Formula Resistor-Capacitor Circuit Time constant    Capacitance    Electrical Resistance

Time constant

Unit
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 $$\tau$$.

Capacitance

Unit
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

Unit
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%.