When a coil is connected across a 20 V dc supply, it draws a current of 5 A . When it is connected across 20 V , 50 Hz ac supply, it draws a current of 4 A . The self inductance of the coil is mH . (Take π=3 )

Physics · Electromagnetic Induction

JEE Main 2024 — 9 April, Shift 1 — Question 57

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

Answer: 10

Numerical answer — enter this value.

Step-by-step solution

Case 1:

\mathrm{i}=\frac{20}{\mathrm{R}} \Rightarrow \mathrm{R}=4 \Omega

Case 2:

\mathrm{i}=\frac{20}{\mathrm{Z}}

$4=\frac{20}{\sqrt{\mathrm{R}^{2}+\mathrm{X}_{\mathrm{L}}^{2}}} \Rightarrow \sqrt{\mathrm{R}^{2}+\mathrm{X}_{\mathrm{L}}^{2}}=5$

$\mathrm{R}^{2}+\mathrm{X}_{\mathrm{L}}^{2}=25 \Rightarrow \mathrm{X}_{\mathrm{L}}=3 \Omega$

$\mathrm{L}=\frac{3}{2 \pi \mathrm{f}}=\frac{1}{2 \times 50}=\frac{1000}{100} \mathrm{mH}$ $\mathrm{L}=10 \mathrm{mH}$

Answer key and solution verified before publishing.

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Exam: JEE Main 2024
Paper: 9 April, Shift 1
Subject: Physics
Chapter: Electromagnetic Induction
Topic: L-R, L-C and L-C-R circuits with DC supply