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Power in AC circuits
Appears in
Concepts tested here
- Average power and power factor
- Power factor
All Questions
2015 AIPMT-I 1 question
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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 beWith R only: $P = \frac{E^2}{R}$ (rms values)
With L in series: $P' = EI\cos\phi = E\cdot\frac{E}{Z}\cdot\frac{R}{Z} = \frac{E^2R}{Z^2}$
$\frac{P'}{P} = \frac{R^2}{Z^2}$
$P' = P\left(\frac{R}{Z}\right)^2$
2012 AIPMT-MAINS 1 question
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The instantaneous values of alternating current and voltages in a circuit are given as $i = \frac{1}{\sqrt2}\sin(100\pi t)$ ampere and $e = \frac{1}{\sqrt2}\sin\left(100\pi t + \frac{\pi}{3}\right)$ volt. The average power in Watts consumed in the circuit is$P = V_{rms}I_{rms}\cos\phi = \frac{1}{2}V_0I_0\cos\phi$
$V_0 = \frac{1}{\sqrt2}$ V, $I_0 = \frac{1}{\sqrt2}$ A, $\phi = \frac{\pi}{3}$
$P = \frac{1}{2}\times\frac{1}{\sqrt2}\times\frac{1}{\sqrt2}\times\cos\frac{\pi}{3} = \frac{1}{2}\times\frac{1}{2}\times\frac{1}{2}$
$P = \frac{1}{8}$ W