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  4. In an L R circuit f=50 Hz, L=2 H, E=5 volts, R=1 Ω then energy stored inductor is

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Q. In an $L R$ circuit $f=50\, Hz,\, L=2\, H,\, E=5$ volts, $R=1\, \Omega$ then energy stored inductor is

BITSATBITSAT 2019

Solution:

$L =2 H , E =5$ volts, $R =1\, \Omega$
Energy in inductor $=\frac{1}{2} LI ^{2}$
$I =\frac{ E }{ Z }$
$I=\frac{5}{\sqrt{R^{2}+(\omega L)^{2}}}=\frac{5}{\sqrt{1+4 \pi^{2} \times 50^{2} \times 4}}$
$=\frac{5}{\sqrt{1+(200 \pi)^{2}}}=\frac{5}{200 \pi}$
Energy $=\frac{1}{2} \times 2 \times \frac{5 \times 5}{200 \times 200 \pi^{2}}$
$=6.33 \times 10^{-5}$