11. 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: (2015)
Solution:
Initially, power dissipated in resistance is $P = \frac{V_{rms}^2}{R}$. When inductance is connected in series, current is $I_{rms} = \frac{V_{rms}}{Z}$ and power factor is $\cos\phi = \frac{R}{Z}$. New power drawn is $P' = V_{rms} I_{rms} \cos\phi = V_{rms} \left(\frac{V_{rms}}{Z}\right) \left(\frac{R}{Z}\right) = \frac{V_{rms}^2 R}{Z^2} = P \left(\frac{R}{Z}\right)^2$.
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