First slide

Power in a.c. circuit

Question

$\frac{2 .5}{π} μF$ capacitor and 3000 ohm resistor are joined in series to an AC source of 200 volt and $50 \sec^{- 1}$ frequency. The power factor of the circuit and the power dissipated in it will respectively be

Moderate

A

0.6, 0.06 W
B

0.06, 0.6 W
C

0.6, 4.8 W
D

4.8, 0.6 W

Solution

$Z = \sqrt{R^{2} + {(\frac{1}{2 πvC})}^{2}}$
$= \sqrt{(3000)^{2} + \frac{1}{{(2 π \times 50 \times \frac{2 .5}{π} \times 10^{- 6})}^{2}}}$
$Z = \sqrt{(3000)^{2} + (4000)^{2}} = 5 \times 10^{3} Ω$
So, power factor, $cosϕ = \frac{R}{Z} = \frac{3000}{5 \times 10^{3}} = 0 .6$
Now, $P = V_{rms} i_{rms} cosϕ = \frac{V_{rms}^{2} cosϕ}{Z}$
$\Rightarrow P = \frac{(200)^{2} \times 0 .6}{5 \times 10^{3}} = 4 .8 W$

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