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Alternating Current question

2022 · 29 Jun · Shift 1 · Q50
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Alternating Current question

2022 · 29 Jun · Shift 1 · Q50

JEE MainPhysicsAlternating CurrentMCQ+4 / −1
For a series LCR circuit, I vs ω\omegaω curve is shown : (a) To the left of ω\omegaω r, the circuit is mainly capacitive. (b) To the left of ω\omegaω r, the circuit is mainly inductive. (c) At ω\omegaω r, impedance of the circuit is equal to the resistance of the circuit. (d) At ω\omegaω r, impedance of the circuit is 0. JEE Main 2022 (Online) 29th June Morning Shift Physics - Alternating Current Question 93 English Choose the most appropriate answer from the options given below :
  1. A
    (a) and (d) only.
  2. B
    (b) and (d) only.
  3. C
    (a) and (c) only.
  4. D
    (b) and (c) only.
View written solutionFree

Correct answer: C

  1. Series LCR circuit current

For a series LCR circuit, the current amplitude is

I=VZI = \frac{V}{Z}I=ZV​

where the impedance is

Z=R2+(ωL−1ωC)2.Z = \sqrt{R^2 + \left(\omega L - \frac{1}{\omega C}\right)^2 }.Z=R2+(ωL−ωC1​)2​.

The current is maximum at resonance frequency ωr\omega_rωr​, where

ωrL=1ωrC.\omega_r L = \frac{1}{\omega_r C}.ωr​L=ωr​C1​.
  1. Nature of circuit to the left of resonance

To the left of ωr\omega_rωr​, we have ω<ωr\omega < \omega_rω<ωr​.

Then:

  • inductive reactance: XL=ωLX_L = \omega LXL​=ωL is smaller,
  • capacitive reactance: XC=1ωCX_C = \frac{1}{\omega C}XC​=ωC1​ is larger.

So,

XC>XLX_C > X_LXC​>XL​

which means the net reactance

X=XL−XC<0.X = X_L - X_C < 0.X=XL​−XC​<0.

Hence the circuit behaves mainly capacitive.

So:

  • (a) True
  • (b) False
  1. Impedance at resonance

At ω=ωr\omega = \omega_rω=ωr​,

ωrL=1ωrC\omega_r L = \frac{1}{\omega_r C}ωr​L=ωr​C1​

so the reactances cancel.

Thus,

Z=R2+02=R.Z = \sqrt{R^2 + 0^2} = R.Z=R2+02​=R.

Therefore:

  • (c) True
  • (d) False

Impedance is minimum at resonance, but it is equal to RRR, not zero.

  1. Correct combination

The correct statements are:

(a) and (c)(a) \text{ and } (c)(a) and (c)

So the correct option is

C\boxed{\text{C}}C​
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