Q23 of 30 Page 1

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?


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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