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Question

A resistance R draws power P when connected to an AC source. If an inductance is now placed in series with the resistance, such that the impedance of the circuit becomes Z, the power drawn will be


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Solution

Power of an alternating circuit

  1. Power of an alternating circuit carrying current I with resistance R, impedance V is defined by the form, P=VrmsZ2R, where, Vrms is the square the root of the time average of the voltage squared.
  2. Impedance of an LR circuit is Z=R2+ωL2, where, R is the resistance and ωL is the inductive reactance due to the inductor L.

Diagram

Power of the circuit

In the absence of the inductance, the power of the circuit is given by

P=VrmsR2R................(1).

When the inductance is connected with the resistance in series, then power is

P'=VrmsZ2R................(2)

Comparing (1) and (2) we get,

P'P=VrmsZ2RVrmsR2R=RZ2orP'=PRZ2

Therefore, the power will be P'=PRZ2.


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