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JEE Main 202125 FebruaryMorning Shift
Exam
JEE Main
Year
2021
Date
25 February
Shift
Morning Shift
Subject
Physics
Chapter
Alternating Current

JEE Main 2021 · 25 February · Morning Shift · Physics · Alternating Current

The angular frequency of alternating current in a L-C-R circuit is...

The angular frequency of alternating current in a L-C-R circuit is 100rads−1100rad{s}^{- 1}. The components connected are shown in the figure. Find the value of inductance of the coil and capacity of condenser.

The angular frequency of alternating current in a L-C-R circuit is 100rad s ^ - 1 . The components connected are shown

Options

  1. A1.33H1 . 33H and 150\muF150\muF
  2. B0.8H0 . 8H and 150\muF150\muF
  3. C1.33H1 . 33H and 250\muF250\muF
  4. D0.8H0 . 8H and 250\muF250\muF

Correct answer

D. 0.8H0 . 8H and 250\muF250\muF

Step-by-step solution

Current through 60Ω60Ω resistance =1560=14A= \dfrac{15}{60} = \dfrac{1}{4}A

thus capacitor current =14A= \dfrac{1}{4}A

∵VC=IXC∵ {V}_{C} = I{X}_{C}

10=14×1\omegaC10 = \dfrac{1}{4} \times \dfrac{1}{\omegaC}

∴C=140ω=14000=250\muF∴ C = \dfrac{1}{40\omega} = \dfrac{1}{4000} = 250\muF

Now,

current through 40Ω40Ω resistance =2040=12A= \dfrac{20}{40} = \dfrac{1}{2}A

thus current through inductor =12−14=14A= \dfrac{1}{2} - \dfrac{1}{4} = \dfrac{1}{4}A

VL=IXL=14×\omegaL{V}_{L} = I{X}_{L} = \dfrac{1}{4} \times \omegaL

20=14×100×L20 = \dfrac{1}{4} \times 100 \times L

⇒L=0.8H⇒ L = 0 . 8H

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