JEE PYQ: Alternating Current Question 27
Question 27 - 2020 (07 Jan Shift 1)
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) $L \leftrightarrow m, C \leftrightarrow k, R \leftrightarrow b$ (b) $L \leftrightarrow \frac{1}{b}, C \leftrightarrow \frac{1}{m}, R \leftrightarrow \frac{1}{k}$ (c) $L \leftrightarrow k, C \leftrightarrow b, R \leftrightarrow m$ (d) $L \leftrightarrow m, C \leftrightarrow \frac{1}{k}, R \leftrightarrow b$
Show Answer
Answer: (d)
Solution
Comparing $m\frac{d^2x}{dt^2} + b\frac{dx}{dt} + kx = 0$ with $L\frac{d^2q}{dt^2} + R\frac{dq}{dt} + \frac{q}{C} = 0$: $L \leftrightarrow m$, $C \leftrightarrow \frac{1}{k}$, $R \leftrightarrow b$.
BETA
