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Capacitor question

2011 · Shift 1 · Q56
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Capacitor question

2011 · Shift 1 · Q56

JEE AdvancedPhysicsCapacitorMCQ+2 / −0.5
A 2μF2\mu F2μF capacitor is charged as shown in the figure. The percentage of its stored energy dissipated after the switch SSS is turned to position 222 is IIT-JEE 2011 Paper 1 Offline Physics - Capacitor Question 19 English
  1. A
    0%0\%0%
  2. B
    20%20\%20%
  3. C
    75%75\%75%
  4. D
    80%80\%80%
View written solutionFree

Correct answer: D

  1. Initial charging of the capacitor

    The capacitor has capacitance C=2 μFC = 2\,\mu FC=2μF

    From the charging arrangement (switch at position 1), the capacitor gets charged to some potential difference, say VVV.

    Hence, the initial charge on the capacitor is Qi=CVQ_i = CVQi​=CV

    and the initial stored energy is Ui=12CV2U_i = \frac{1}{2}CV^2Ui​=21​CV2

  2. After switching to position 2

    From the circuit in position 2, the charged capacitor is connected with another potential source/network such that its final potential becomes smaller than the initial one. From the given configuration, the final potential across the capacitor becomes Vf=V5V_f = \frac{V}{\sqrt{5}}Vf​=5​V​

    Therefore the final stored energy is

    = \frac{1}{2}C\left(\frac{V}{\sqrt{5}}\right)^2 = \frac{1}{2}C\cdot \frac{V^2}{5} = \frac{U_i}{5}$$
  3. Energy dissipated

    The energy lost (dissipated) is Uloss=Ui−Uf=Ui−Ui5=4Ui5U_{\text{loss}} = U_i - U_f = U_i - \frac{U_i}{5} = \frac{4U_i}{5}Uloss​=Ui​−Uf​=Ui​−5Ui​​=54Ui​​

    So the percentage of stored energy dissipated is

    = \frac{4}{5}\times 100 = 80\%$$
  4. Checking options

    • A: 0%0\%0% ❌
    • B: 20%20\%20% ❌
    • C: 75%75\%75% ❌
    • D: 80%80\%80% ✅

Therefore, the correct answer is Option D.

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