# Formula Resistor-Capacitor Circuit Time constant Capacitance Electrical Resistance

## 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

`$$ \mathrm{F} = \frac{ \mathrm{C} }{ \mathrm{V} } $$`

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

`$$ R $$`Unit

`$$ \mathrm{\Omega} = \frac{ \mathrm{kg} \, \mathrm{m}^2 }{ \mathrm{A}^2 \, \mathrm{s}^3 } $$`

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%.