Exam

JEE Main

Year

2020

Date

7 January

Shift

Morning Shift

Subject

Physics

Chapter

Alternating Current

JEE Main 2020 · 7 January · Morning Shift · Physics · Alternating Current

A LCR circuit behaves like a clamped harmonic oscillator. Comparing...

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

Step-by-step solution

In damped oscillation $ma + bv + kx = 0$

$m\dfrac{{d}^{2}x}{d{t}^{2}} + b\dfrac{dx}{dt} + kx = 0 \ldots . . \left(i\right)$
In the circuit
$- iR - L\dfrac{di}{dt} - \dfrac{q}{c} = 0$
$L\dfrac{{d}^{2}q}{d{t}^{2}} + R\dfrac{dq}{dt} + \dfrac{1}{c} . q = 0 . . \left(ii\right)$
Comparing equation (i) and (ii)
$m = L, b = R, k = \dfrac{1}{c}$