First slide

Power in a.c. circuit

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

Difficult

A

$P (\frac{R}{Z})$
B

P
C

$P {(\frac{R}{Z})}^{2}$
D

$P \sqrt{\frac{R}{Z}}$

Solution

$P = V_{rms} I_{rms}$
$= V_{rms} \times \frac{V_{rms}}{R}$

$P = \frac{V_{rms}^{2}}{R} \Rightarrow V_{rms}^{2} = PR . . . . (i)$
$Case II : Power drawn in LR circuit$
$P^{'} = V_{rms} I_{rms} cosϕ = V_{rms} \times \frac{V_{rms}}{Z} \times \frac{R}{Z}$
$= V_{rms}^{2} \frac{R}{Z^{2}} = PR \times \frac{R}{Z^{2}}$ (using eqn. (i))
$P^{'} = P \frac{R^{2}}{Z^{2}}$

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