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  4. An alternating voltage e=200 text sin text 100t is applied to a series combination R=30 Ω and an inductor of 400 mH . The power factor of the circuit is

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Q. An alternating voltage $ e=200\text{ }sin\text{ }100t $ is applied to a series combination $ R=30\,\Omega $ and an inductor of $ 400\, mH $ . The power factor of the circuit is

KEAMKEAM 2008Alternating Current

Solution:

Power factor $ \cos \phi =\frac{R}{\sqrt{{{R}^{2}}+{{\omega }^{2}}{{L}^{2}}}} $
$ =\frac{30}{\sqrt{{{(30)}^{2}}+{{(100)}^{2}}\times {{(400\times {{10}^{-3}})}^{2}}}} $
$ =\frac{30}{\sqrt{900+1600}}=\frac{30}{50}=0.6 $