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JEE Main 20204 SeptemberEvening Shift
Exam
JEE Main
Year
2020
Date
4 September
Shift
Evening Shift
Subject
Physics
Chapter
Capacitance

JEE Main 2020 · 4 September · Evening Shift · Physics · Capacitance

A capacitor C is fully charged with voltage V _ 0 . After...

A capacitor CC is fully charged with voltage V0{V}_{0}. After disconnecting the voltage source, it is connected in parallel with another uncharged capacitor of capacitance C2\dfrac{C}{2}. The energy loss in the process after the charge is distributed between the two capacitors is :A capacitor C is fully charged with voltage V _ 0 . After disconnecting the voltage source, it is connected in parallelA capacitor C is fully charged with voltage V _ 0 . After disconnecting the voltage source, it is connected in parallel

Options

  1. A12CV02\dfrac{1}{2}C{V}_{0}^{2}
  2. B13CV02\dfrac{1}{3}C{V}_{0}^{2}
  3. C14CV02\dfrac{1}{4}C{V}_{0}^{2}
  4. D16CV02\dfrac{1}{6}C{V}_{0}^{2}

Correct answer

D. 16CV02\dfrac{1}{6}C{V}_{0}^{2}

Step-by-step solution

A capacitor C is fully charged with voltage V _ 0 . After disconnecting the voltage source, it is connected in parallel

Heat Loss is given by,&

H=C1C22(C1+C2)(V1−V2)2H = \dfrac{{C}_{1}{C}_{2}}{2\left({C}_{1} + {C}_{2}\right)}\left({V}_{1} - {V}_{2}\right)2

V1{V}_{1}~is& initial voltage of capacitor& C=V0C= {V}_{0}

V2{V}_{2}~is the initial voltage of capacitor& C2=0\dfrac{C}{2}= 0

=c×c22(c+c2)(V0−0)2=C6V02= \dfrac{c \times \dfrac{c}{2}}{2\left(c + \dfrac{c}{2}\right)}\left({V}_{0} - 0\right)2 = \dfrac{C}{6}{V}_{0}^{2}

H=16C0V02H = \dfrac{1}{6}{C}_{0}{V}_{0}^{2}

&

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