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Formula: **Resistor-Capacitor Circuit**

$$\tau ~=~ R \, C$$
$$\tau ~=~ R \, C$$
$$C ~=~ \frac{\tau}{R}$$
$$R ~=~ \frac{\tau}{C}$$

## 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%.