A voltage V=V0 sin ωt is applied to a series LCR circuit. Derive the expression for the average power dissipated over a cycle. Under what condition is
(i) no power dissipated even though the current flows through the circuit,
(ii) maximum power dissipated in the circuit?
Voltage V=V0 sin ωt is applied to a series LCR circuit.
Current is I=I0 sin (ωt+Φ)
Instantaneous power supplied by the source is
P=VI=(V0 sin ωt)×(I0 sin (ωt+Φ))
= V0I02[cos Φ−cos (2ωt+Φ)]
The average power over a cycle is average of the two terms on the R.H.S. of the above equation.
The second term is time dependent, so, its average is zero.
So, P=V0I02cos Φ
= V0I0√2 √2cos Φ
= VI cos Φ
cos Φ is called the power factor.
For pure inductive circuit or pure capacitive circuit, the phase difference between current and voltage i.e., Φ is π2.
So Cos Φ=0
Therefore, no power is dissipated.
For power dissipated at resonance in an LCR circuit,
∴ Cos Φ=1
So, maximum power is dissipated.