Formula: Resistor-Capacitor Circuit Time constant Capacitance Electrical Resistance
$$\tau ~=~ R \, C$$
$$\tau ~=~ R \, C$$
$$C ~=~ \frac{\tau}{R}$$
$$R ~=~ \frac{\tau}{C}$$
Time constant
$$ \tau $$ Unit $$ \mathrm{s} $$
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
$$ C $$ Unit $$ \mathrm{F} $$
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
$$ \class{brown}{R} $$ Unit $$ \mathrm{\Omega} $$
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%.