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A Voltage V = V0 Sin ωt is Applied to a Series LCR Circuit. Derive the Expression for the Average Power Dissipated Over a Cycle. - Physics

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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?

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Voltage V=V0sinωt is applied to an series LCR circuit.

Current is  π2" role="presentation" style="position: relative;">π2



Instantaneous power supplied by the source is




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.





cosϕ  is called the power factor.

Case I

For pure inductive circuit or pure capacitive circuit, the phase difference between current and voltage is `pi/2`


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,

`X_C-X_L=0, phi=0`

∴ cos ϕ = 1

So, maximum power is dissipated.

Concept: Ac Voltage Applied to a Series Lcr Circuit
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