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JEE Main 20202 SeptemberEvening Shift
Exam
JEE Main
Year
2020
Date
2 September
Shift
Evening Shift
Subject
Physics
Chapter
Electromagnetic Induction

JEE Main 2020 · 2 September · Evening Shift · Physics · Electromagnetic Induction

An inductance coil has a reactance of 100Ω . When an AC signal of...

An inductance coil has a reactance of 100Ω100Ω . When an AC signal of frequency 1000Hz1000Hz is applied to the coil, the applied voltage leads the current by 45°45 °. The self-inductance of the coil is

Options

  1. A1.1×10−2H1 . 1 \times {10}^{- 2}H
  2. B1.1×10−1H1 . 1 \times {10}^{- 1}H
  3. C5.5×10−5H5 . 5 \times {10}^{- 5}H
  4. D6.7×10−7H6 . 7 \times {10}^{- 7}H

Correct answer

A. 1.1×10−2H1 . 1 \times {10}^{- 2}H

Step-by-step solution

tanθ=xLR=tan⁡45°tan \theta = \dfrac{{x}_{L}}{R} = \tan 45 °
xL=R{x}_{L} = R
=100=xL2+R2= 100 = \sqrt{{x}_{L}^{2} + {R}^{2}}
100=R2+R2100 = \sqrt{{R}^{2} + {R}^{2}}
2R=100\sqrt{2}R = 100
R=502R = 50\sqrt{2}
∴xL=502∴ {x}_{L} = 50\sqrt{2}
Lω=502L \omega = 50\sqrt{2}
L=5022π×1000=252πmHL = \dfrac{50\sqrt{2}}{2\pi \times 1000} = \dfrac{25\sqrt{2}}{\pi}mH
=1.1×10−2H= 1 . 1 \times {10}^{- 2}H
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