Any linear sinusoidal driven combination of capacitors, inductors, resistors has a steady state solution of the form

which can be found using a complex impedance Z defined by

where I and V are also treated as complex quantities. The current I is given in terms of the electromotive force by


and the phase shift by

For circuit elements in series,

and in parallel,

For capacitors,

where is the angular frequency, Q is the charge, and C is the capacitance. Taking the derivative on each side gives

so

For inductors,

where L is the inductance. Integrating both sides gives

so

For resistors, the impedance is simply equal to the resistance R,