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 (i) no power is dissipated even though the current flows through the circuit, (ii) maximum power is dissipated in the circuit?



Voltage V=V0sinωt is applied to an series LCR circuit. Current is I=I0sin(ωt+ϕ) I0=V0Zϕ=tan-1XC-XLR Instantaneous power supplied by the source is P=VI =(V0sinωt)×(I0sin(ωt+ϕ) =V0I02cosϕ-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. P=V0I02cosϕ =V0I022cosϕ =VIcosϕP=I2Zcosϕ is called the power factor. Case I For pure inductive circuit or pure capacitive circuit, the phase difference between current and voltage is . Therefore, no power is dissipated. This current is sometimes referred to as wattless current. Case II For power dissipated at resonance in an LCR circuit, So, maximum power is dissipated.