Given an electric circuit composed of a resistor with resistance R and a capacitor with capacitance C, the Kirchhoff loop rule requires that the sum of the changes in potential must be zero, so

where I is the current through the resistor and Q is the charge on the capacitor. Differentiating,

and rearranging gives

which is a first order ordinary differential equation with solution

Here, is the current at time t = 0 and is a decay constant defined by

For a sinusoidally driven CR circuit, use the equation of a sinusoidally driven CLR circuit with L = 0

where the phase lag is

so the current leads the voltage. The complete solution is then

where is the permittivity of free space.