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NCERT Class XII Chapter
Electrostatic Potential and Capacitance
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Question : 11 of 37
Marks: +1, -0
A 600 pF capacitor is charged by a 200 V supply. It is then disconnected from the supply and is connected to another uncharged 600 pF capacitor. How much electrostatic energy is lost in the process?
Solution:  
C1C_1 = 600 pF, V1V_1 = 200 V , C2C_2 = 600 pF , V2V_2 = 0
On connecting charged capacitor to uncharged capacitor, the common potential V across the capacitors is
V = C1V1+C2V2C1+C2\frac{C_1V_1+C_2V_2}{C_1+C_2} = 600×10−12×200+0(600+600)×10−12\frac{600 \times 10^{-12} \times 200 + 0}{(600+600) \times 10^{-12}} or V = 100 V
Energy stored in capacitors before connection is
UiU_i = 12C1V12\frac{1}{2} C_1 V_1^2 + 0 = 12\frac{1}{2} × 600 × 10−12×200210^{-12} \times 200^2 or UiU_i = 12 µJ
and 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} (600 + 600) × 10−12×100210^{-12} \times 100^2 or UfU_f = 6 µJ
Hence the energy lost in the process is
Δ = Uf−UiU_f-U_i = (6 - 12) µJ or ΔU = - 6 µJ
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