Given an electric circuit composed of an inductor with inductance L and a capacitor with capacitance C, the Kirchhoff loop rule requires that the sum of the changes in potential must be zero, so
(1)
where I is the current through the inductor and Q is the charge on the capacitor. Differentiating
(2)
and rearranging gives
(3)
which is a first order ordinary differential equation with solution
(4)
Here,
(the current at time t = 0), 
is determined from a combination of 
and 
and
(5)
The current leads the voltage since
(6)
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