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Alternating Current question

2021 · 18 Mar · Shift 1 · Q57
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Alternating Current question

2021 · 18 Mar · Shift 1 · Q57

JEE MainPhysicsAlternating CurrentMCQ+4 / −1
In a series LCR resonance circuit, if we change the resistance only, from a lower to higher value :
  1. A
    The bandwidth of resonance circuit will increase.
  2. B
    The resonance frequency will increase.
  3. C
    The quality factor will increase.
  4. D
    The quality factor and the resonance frequency will remain constant.
View written solutionFree

Correct answer: A

  1. Resonance frequency in a series LCR circuit

For a series LCR circuit, the resonance frequency is

ω0=1LC,f0=12πLC\omega_0 = \frac{1}{\sqrt{LC}}, \qquad f_0 = \frac{1}{2\pi\sqrt{LC}}ω0​=LC​1​,f0​=2πLC​1​

This depends only on LLL and CCC, not on RRR.

So if only resistance is changed, the resonance frequency remains unchanged.

  1. Bandwidth of a series resonance circuit

For a series LCR circuit, bandwidth is

Δω=RL\Delta \omega = \frac{R}{L}Δω=LR​

or in frequency form,

Δf=R2πL\Delta f = \frac{R}{2\pi L}Δf=2πLR​

Thus, when RRR increases, the bandwidth increases.

So Option A is correct.

  1. Quality factor

For a series LCR circuit,

Q=ω0LR=1RLCQ = \frac{\omega_0 L}{R} = \frac{1}{R}\sqrt{\frac{L}{C}}Q=Rω0​L​=R1​CL​​

Hence, if RRR increases, QQQ decreases.

So:

  • Option C is false.
  • Option D is false because although resonance frequency remains constant, quality factor does not remain constant.
  1. Checking all options
  • A: Bandwidth increases when RRR increases. ✅ Correct
  • B: Resonance frequency increases. ❌ False
  • C: Quality factor increases. ❌ False
  • D: Quality factor and resonance frequency both remain constant. ❌ False
  1. Final answer

The correct option is:

A\boxed{\text{A}}A​
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