Bandwidth and Resonance Sharpness – Rankers Physics

LR, RC and LCR Circuits: Practice Problem & Solution

Assertion (A): Smaller the band width, sharper the resonance and easier it is to tune an \(LCR\) circuit. Reason (R): Resonant frequency is arithmetic mean of half power frequencies.  
Both (A) & (R) are true and the (R) is the correct explanation of the (A)
Both (A) & (R) are true but the (R) is not the correct explanation of the (A)
(A) is true but (R) is false
Both (A) and (R) are false

Short Solution (Best for NEET):

To solve this problem, we apply the core principles of LR, RC and LCR Circuits. Understanding the underlying formula is key to arriving at the correct answer below:

Smaller bandwidth implies a higher quality factor \(Q\) and sharper resonance, leading to better frequency selectivity (easier tuning). Resonant frequency \(\omega_0\) is the *geometric mean* \(sqrt{\omega_1 \omega_2}\,\) not the arithmetic mean of half-power frequencies.

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