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JEE Main 20154 April
Exam
JEE Main
Year
2015
Date
4 April
Subject
Physics
Chapter
Alternating Current

JEE Main 2015 · 4 April · Physics · Alternating Current

An LCR circuit is equivalent to a damped pendulum. In an LCR...

An LCR circuit is equivalent to a damped pendulum. In an LCR circuit the capacitor is charged to Q0{Q}_{0} and then connected to the L and R as shown below:
An LCR circuit is equivalent to a damped pendulum. In an LCR circuit the capacitor is charged to Q _ 0 and then
If a student plots graphs of the square of maximum charge \left({Q}_\max^{2}\right) on the capacitor with time (t) for two different values L1andL2(L1>L2){L}_{1} and {L}_{2} ( {L}_{1} > {L}_{2} ) of L then which of the following represents this graph correctly? (plots are schematic and not drawn to scale)

Options

  1. AThickening of arteries due to cholesterol deposition is
  2. BThickening of arteries due to cholesterol deposition is
  3. CThickening of arteries due to cholesterol deposition is
  4. DThickening of arteries due to cholesterol deposition is

Correct answer

C. Thickening of arteries due to cholesterol deposition is

Step-by-step solution

Comparing to the damped pendulum. We write,& mdvdt=−kx−bv\text{m}\dfrac{\text{d}\text{v}}{\text{d}\text{t}} = - \text{kx} - \text{bv}, bvbv is resistive force,⇒⇒~Amplitude,& A=A0e−bt2m\text{A} = {A}_{0}e^{- \dfrac{bt}{2\text{m}}}. Comparing results, we can write

qc=+Ldidt+iR\dfrac{q}{c} = + \text{L}\dfrac{\text{d}\text{i}}{\text{d}\text{t}} + \text{iR}, as charge decreasing,~
An LCR circuit is equivalent to a damped pendulum. In an LCR circuit the capacitor is charged to Q _ 0 and then

qc=Ld2qdt2−dqdtR\dfrac{q}{c} = \text{L}\dfrac{d^{2}\text{q}}{\text{d}t^{2}} - \dfrac{\text{d}\text{q}}{\text{d}\text{t}}\text{R}

⇒A=q;R=b,m=L⇒ \text{A} = \text{q}\text{;}\text{R} = \text{b}\text{,}\text{m} = \text{L}
⇒q=q0e−Rt2L⇒q2=q02e−RtL⇒q2=q02e−RtL\text{⇒}\text{q} = {q}_{0}e^{- \dfrac{Rt}{2\text{L}}}\text{⇒}q^{2} = {q}_{0}^{2}e^{- \dfrac{Rt}{L}}\text{⇒}q^{2} = {q}_{0}^{2}e^{- \dfrac{Rt}{L}}.

Exponentially decreasing function, L1{L}_{1} graph has higher values than~L2{L}_{2}.
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