In an LCR series circuit an alternating voltage source of frequency F is connected. The current leads the voltage by 45°. The value of L is (a) (1 + 2π FCR)/(2π FC) (b) (1 + 2π FCR)/(4π² F² C) (c) (1 - 2π FCR)/(4π² F² C) (d) (1 + 2π FR)/(4π² F² C)

Answer: (c). Current leads by 45°: tan 45° = (XC - XL)/(R) ⇒ XL = XC - R. 2π FL = (1)/(2π FC) - R = (1 - 2π FCR)/(2π FC) L = (1 - 2π FCR)/(4π²F²C) So the answer is (c).

In an LCR series circuit an alternating voltage source of frequency F… | MHT CET 2026 (20 Apr, Shift 2)

Q10MHT CET 2026 · 20 APR · SHIFT 2Medium

Series LCR Circuit

In an LCR series circuit an alternating voltage source of frequency $F$ is connected. The current leads the voltage by $45^\circ$ . The value of $L$ is

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Answer: (c)

Current leads by $45^\circ$ : $\tan 45^\circ = \dfrac{X_C - X_L}{R} \Rightarrow X_L = X_C - R$ .
$2\pi FL = \dfrac{1}{2\pi FC} - R = \dfrac{1 - 2\pi FCR}{2\pi FC}$
$L = \dfrac{1 - 2\pi FCR}{4\pi^2F^2C}$
So the answer is (c).

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