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7.Alternating Current
hard
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 $\pi=3$ )
A
$8$
B
$7$
C
$9$
D
$10$
(JEE MAIN-2024)
Solution
(Imaqge)
Case-$I$:
$\mathrm{i}=\frac{20}{\mathrm{R}} \Rightarrow \mathrm{R}=4 \Omega$
Case-$II$:
(Image)
$i=\frac{20}{Z}$
$4=\frac{20}{\sqrt{R^2+X_L^2}} \Rightarrow \sqrt{R^2+X_L^2}=5$
$R^2+X_L^2=25 \Rightarrow X_L=3 \Omega$
$L=\frac{3}{2 \pi f}=\frac{1}{2 \times 50}=\frac{1000}{100} m H$
$L=10 m H$
Standard 12
Physics
