JEE Main · 2020 · 07 Jan 2020 · Shift 1 · Alternating Current

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A LCR circuit behaves like a damped harmonic oscillator. Comparing it with a physical spring-mass damped oscillator having damping constant 'b', the correct equivalence would be:

(A) $L \leftrightarrow \frac{1}{b}$ , $C \leftrightarrow \frac{1}{m}$ , $R \leftrightarrow \frac{1}{k}$
(B) $L \leftrightarrow k$ , $C \leftrightarrow b$ , $R \leftrightarrow m$
(C) $L \leftrightarrow m$ , $C \leftrightarrow \frac{1}{k}$ , $R \leftrightarrow b$ ✓ Correct
(D) $L \leftrightarrow m$ , $C \leftrightarrow k$ , $R \leftrightarrow b$

Answer: (C)

Solution

Writing the equations of motion side by side, the damped spring–mass system is

m \overset{x}{¨} + b \overset{x}{˙} + k x = 0

while the series

L C R

loop is

L \overset{q}{¨} + R \overset{q}{˙} + \frac{1}{C} q = 0

. Matching term by term, the inductance plays the role of the mass, the resistance that of the damping constant, and the reciprocal capacitance that of the spring constant:

L \leftrightarrow m

R \leftrightarrow b

and

C \leftrightarrow \frac{1}{k}

JEE Main · 2020 · 07 Jan 2020 · Shift 1 · Single correct option

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JEE Main · 2020 · 07 Jan 2020 · Shift 1 · Alternating Current

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