JEE Mains · Physics · STD 11 - 13. oscillations
A \(LCR\) circuit behaves like a damped harmonic oscillator. Comparing it with a physical springmass damped oscillator having damping constant \(\mathrm{b}\), the correct equivalence would be:
- A \(\mathrm{L} \leftrightarrow \mathrm{m}, \mathrm{C} \leftrightarrow \frac{1}{\mathrm{k}}, \mathrm{R} \leftrightarrow \mathrm{b}\)
- B \(\mathrm{L} \leftrightarrow \frac{1}{\mathrm{b}}, \mathrm{C} \leftrightarrow \frac{1}{\mathrm{m}}, \mathrm{R} \leftrightarrow \frac{1}{\mathrm{k}}\)
- C \(\mathrm{L} \leftrightarrow \mathrm{m}, \mathrm{C} \leftrightarrow \mathrm{k}, \mathrm{R} \leftrightarrow \mathrm{b}\)
- D \(\mathrm{L} \leftrightarrow \mathrm{k}, \mathrm{C} \leftrightarrow \mathrm{b}, \mathrm{R} \leftrightarrow \mathrm{m}\)
Answer & Solution
Correct Answer
(A) \(\mathrm{L} \leftrightarrow \mathrm{m}, \mathrm{C} \leftrightarrow \frac{1}{\mathrm{k}}, \mathrm{R} \leftrightarrow \mathrm{b}\)
Step-by-step Solution
Detailed explanation
By \(kVL\) \(-\mathrm{L} \frac{\mathrm{di}}{\mathrm{dt}}-\frac{\mathrm{q}}{\mathrm{C}}-\mathrm{iR}=0\) \(\mathrm{L} \frac{\mathrm{d}^{2} \mathrm{q}}{\mathrm{dt}^{2}}+\frac{1}{\mathrm{C}} \mathrm{q}+\mathrm{R} \frac{\mathrm{dq}}{\mathrm{dt}}=0\) for damped oscillator net force…
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