First slide

AC Circuits

Question

A virtual current of 4A and 50 Hz flows in an ac circuit containing a coil. The power consumed in the coil is 240 W. If the virtual voltage across the coil is 100 V its inductance will be

Moderate

A

$\frac{1}{3 π} H$
B

$\frac{1}{5 π} H$
C

$\frac{1}{7 π} H$
D

$\frac{1}{9 π} H$

Solution

$R = \frac{P}{i_{rms}^{2}} = \frac{240}{16} = 15 Ω$
$Z = \frac{V}{i} = \frac{100}{4} = 25 Ω$
Now $X_{L} = \sqrt{Z^{2} - R^{2}} = \sqrt{{(25)}^{2} - {(15)}^{2}} = 20 Ω$
$∴ 2 πνL = 20 \Rightarrow L = \frac{20}{2 π \times 50} = \frac{1}{5 π} H$

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