# (a) Obtain the expression for the average power dissipated in series LCR circuit driven by an AC source of voltage (b) Define the terms: (i) Wattless current and (ii) Q-factor of LCR circuit

(a) Given,

Voltage,

Current

where  is the phase difference between current and applied voltage,

where,

Hence, the instantaneous power is

................(1)

The average of the second term of the equation is zero

Therefore,

Average power dissipated over a complete cycle

This can be also be written as

(b) (i) Wattless current

In a purely inductive or capacitive circuit, the phase difference between voltage and current is . Then the power factor  which means power dissipated in the circuit is zero even though the current is flowing in the circuit. Such type of current is known as Wattles's current.

(ii) Q - factor of LCR circuit

Q - factor of LCR circuit is the sharpness of resonance in a circuit it is given by,

where  is the resonant frequency.

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