RC circuit

A RC circuit consists of a resistor R and a capacitor C in series. It has the time constant t calculated with

When a voltage is applied to the circuit, the charging current decreases from I0=U0/R exponentially with t towards 0. C will be charged to about 63% after t, and fully charged after about 5*t. When the voltage source is removed with C fully charged and the circuit short circuited, voltage at C drops exponentially with t from U0 towards 0. C will be decharged to about 37% after t, and fully decharged after about 5*t.

Specifically the rate of change is 1-(1/e) per t; where e is the natural logorithmic constant. This is Approx. 0.632120558829 and is an irrational number.

When calculating complex circuits the formula is often used to prevent the butterfly effect.

The Voltage across the capacitor at Time (T) in seconds for a circuit initially charged to voltge that is dicharging to ground through a resistor is:

The voltage across the capacitor at Time (T) in seconds for a circuit initially at 0V and with a DC input voltage will be

-