LR, RC and LCR Circuits: Practice Problem & Solution

Assertion (A): If the resistance of a series resonant LCR circuit is decreased, then the peak current versus frequency graph will be taller and narrower. Reason (R): If the resistance of a series resonant LCR circuit decreased, then its resonance will be unaffected.

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

Solution Explained:

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:

When resistance \(R\) in a series \(LCR\) circuit decreases, the peak current \(I_{max} = V/R\) at resonance increases, making the peak taller. The quality factor \(Q = (\omega_0 L)/R\) increases, leading to a narrower resonance curve. The resonant frequency \(omega_0 = 1/\sqrt{LC}\) remains unchanged, but the overall resonance behavior (sharpness, peak current) is affected. Therefore, (A) is true and (R) is false.

LR, RC and LCR Circuits: Practice Problem & Solution

Solution Explained:

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