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NCERT Class XII Chapter
Electrostatic Potential and Capacitance
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Question : 27 of 37
Marks: +1, -0
A 4 μF capacitor is charged by a 200 V supply. It is then disconnected from the supply, and is connected to another uncharged 2 μF capacitor. How much electrostatic energy of the first capacitor is lost in the form of heat and electromagnetic radiation?
Solution:  
C1C_1 = 4 µF , V1V_1 = 200 V , C2C_2 = 2 µF , V2V_2 = 0
So, common potential difference across the two capacitors after connection is
V = C1V1+C2V2C1+C2\frac{C_1V_1+C_2V_2}{C_1+C_2} = 4×106×200+0(4+2)×106\frac{4\times10^{-6}\times200+0}{(4+2)\times10^{-6}} = 133.33 V
Initially, total energy stored in capacitors before connection is
UiU_i = 12C1V12\frac{1}{2} C_1V_1^2 = 12\frac{1}{2} × 4 × 106×200210^{-6} \times 200^2 = 0.08 J
and total energy stored in capacitors after connection is
UfU_f = 12(C1+C2)V2\frac{1}{2} (C_1+C_2)V^2 = 12\frac{1}{2} (4 + 2) × 106×133.33210^{-6} \times 133.33^2 or UfU_f = 0.053 J
So, energy lost due to connection is
ΔU = UfUiU_f-U_i = 0.053 - 0.08 or ΔU = - 0.027 J
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