Question 121 of 153

When a coil is connected across a $20 \mathrm{~V}$ dc supply, it draws a current of $5 \mathrm{~A}$. When it is connected across $20 \mathrm{~V}, 50 \mathrm{~Hz}$ ac supply, it draws a current of $4 \mathrm{~A}$. The self inductance of the coil is ______ $\mathrm{mH}$. $($ Take $\pi=3$ )

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Answer: 10

Case-I:

$i=\frac{20}{R} \Rightarrow R=4 \Omega$
Case-II:
$\begin{aligned} & \mathrm{i}=\frac{20}{\mathrm{Z}} \\ & 4=\frac{20}{\sqrt{\mathrm{R}^2+\mathrm{X}_{\mathrm{L}}^2}} \Rightarrow \sqrt{\mathrm{R}^2+\mathrm{X}_{\mathrm{L}}^2}=5 \\ & \mathrm{R}^2+\mathrm{X}_{\mathrm{L}}^2=25 \Rightarrow \mathrm{X}_{\mathrm{L}}=3 \Omega \\ & \mathrm{L}=\frac{3}{2 \pi \mathrm{f}}=\frac{1}{2 \times 50}=\frac{1000}{100} \mathrm{mH} \\ & \mathrm{L}=10 \mathrm{mH}\end{aligned}$