(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.