Verified Solution • 2025–26 Session moderate

QJEEM21Ph55ac: JEE Main 2021 Physics - Class 12 JEEM21Ph55ac Solution: In a series LCR resonance circuit, if we change the resistance…

In a series LCR resonance circuit, if we change the resistance only, from a lower to higher value :

Multiple Choice Options

  • A The bandwidth of resonance circuit will increase.
  • B The resonance frequency will increase.
  • C The quality factor will increase.
  • D The quality factor and the resonance frequency will remain constant.

Step-by-Step Verified Solution

ω=1LC{\omega } = {1 \over {\sqrt {LC} }}

⇒\Rightarrow 2 π\pi f = 1LC{1 \over {\sqrt {LC} }}

⇒\Rightarrow f = 12πLC{1 \over {2\pi \sqrt {LC} }}

f does not depends on resistance(R).

Quality factor, Q=ωLRQ = {{\omega L} \over R}

⇒\Rightarrow Q∝1RQ \propto {1 \over R}

So if R increase then Q will decrease.

Also, Q=ωLR=ωΔβQ = {{\omega L} \over R} = {\omega \over {\Delta \beta}}

where Δβ\Delta \beta = bandwidth

Δβ=RL\Delta \beta = {R \over L}

So if R increase then Δβ\Delta \beta will increase too.

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