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JEE Advanced 2011Paper 1
Exam
JEE Advanced
Year
2011
Paper
Paper 1
Subject
Physics
Chapter
Capacitance

JEE Advanced 2011 · Paper 1 · Physics · Capacitance

A 2 μ F capacitor is charged as shown in the figure. The percentage...

A 2μF2 \mu \mathrm{F} capacitor is charged as shown in the figure. The percentage of its stored energy dissipated after the switch SS is turned to position 2 , is A 2 μ F capacitor is charged as shown in the figure. The percentage of its stored energy dissipated after the switch S

Options

  1. A0%0 \%
  2. B20%20 \%
  3. C75%75 \%
  4. D80%80 \%

Correct answer

D. 80%80 \%

Step-by-step solution

q_i=C_i V=2 V=q(say)Thischargewillremainconstantafterswitchisshiftedfromposition1toposition2.(say) This charge will remain constant after switch is shifted from position 1 to position 2.Ui=12q2Ci=q22×2=q24Uf=12q2Cf=q22×10=q220\begin{aligned}U_i & =\frac{1}{2} \frac{q^2}{C_i}=\frac{q^2}{2 \times 2}=\frac{q^2}{4}\\ U_f & =\frac{1}{2} \frac{q^2}{C_f}=\frac{q^2}{2 \times 10}=\frac{q^2}{20} \end{aligned}∴\therefore Energy dissipated =Ui−Uf=q25=U_i-U_f=\frac{q^2}{5} This energy dissipated (=q25)\left(=\frac{q^2}{5}\right) is 80%80 \% of the initial stored energy \left(=\frac{q^2}{4}\right)$. Analysis of Question (i) This question is moderately tough. (ii) In a capacitor circuit, redistribution of charge takes place under following three conditions. (a) A switch is closed. (b) A closed switch is opened. (c) A switch is shifted from one position to another position. In the redistribution of charge, energy is dissipated.
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