# A voltage V = V<s

The voltage given is, V = V0 sin ωt

The net impedance of the circuit is,

The current in the circuit is,

Where,

So, the instantaneous power can be written as,

Using the trigonometric identity,

We get,

So, average power is,

The above integral evaluates to,

Case 1:

For a pure inductive circuit or pure capacitive circuit, the phase difference between the current and voltage, Φ=ϖ/2

So,

The power dissipated is Zero

Case 2:

For power dissipated at resonance in an LCR circuit.

Xc-Xl=0, Φ=0

Cos Φ=1

So, Maximum power is dissipated by the resistance.

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