First slide

Phasors and Phasor Diagrams

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

$\frac{1}{{3\pi }} H$
B

$\frac{1}{{5\pi }} H$
C

$\frac{1}{{7\pi }} H$
D

$\frac{1}{{9\pi }} H$

Solution

$R = \frac{P}{{i_{rms}^2}} = \frac{{240}}{{16}} = 15\Omega$
$Z = \frac{V}{i} = \frac{{100}}{4} = 25\Omega$
$Now\,\,{X_L} = \sqrt {{Z^2} - {R^2}} = \sqrt {{{(25)}^2} - {{(15)}^2}} = 20\Omega$
$\therefore 2\pi \nu L = 20 \Rightarrow L = \frac{{20}}{{2\pi \times 50}} = \frac{1}{{5\pi }}Hz$

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