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Alternating Current question

2021 · 25 Feb · Shift 1 · Q49
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Alternating Current question

2021 · 25 Feb · Shift 1 · Q49

JEE MainPhysicsAlternating CurrentMCQ+4 / −1
The angular frequency of alternating current in a L-C-R circuit is 100 rad/s. The components connected are shown in the figure. Find the value of inductance of the coil and capacity of condenser. JEE Main 2021 (Online) 25th February Morning Shift Physics - Alternating Current Question 130 English
  1. A
    0.8 H and 150 μ\muμ F
  2. B
    0.8 H and 250 μ\muμ F
  3. C
    1.33 H and 150 μ\muμ F
  4. D
    1.33 H and 250 μ\muμ F
View written solutionFree

Correct answer: NONE OF THE GIVEN OPTIONS IS CORRECT FOR $\OMEGA = 100\ \TEXT{RAD/S}$ UNDER THE STANDARD RESONANCE CONDITION. IF THE INTENDED FREQUENCY WERE ABOUT $70.7\ \TEXT{RAD/S}$, THEN OPTION B (OR C APPROXIMATELY) WOULD FIT BETTER. THE STORED ANSWER B DOES NOT AGREE WITH THE CALCULATION.

  1. Use the resonance condition for an L-C-R circuit

For an alternating current circuit, the angular frequency at resonance is

ω=1LC\omega = \frac{1}{\sqrt{LC}}ω=LC​1​

Given:

ω=100 rad/s\omega = 100\ \text{rad/s}ω=100 rad/s

So,

100=1LC100 = \frac{1}{\sqrt{LC}}100=LC​1​

Squaring both sides:

1002=1LC100^2 = \frac{1}{LC}1002=LC1​ LC=110000=10−4LC = \frac{1}{10000} = 10^{-4}LC=100001​=10−4

Thus, the product LCLCLC must be

LC=10−4LC = 10^{-4}LC=10−4
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