Electrostatics Question 105

Question: Two insulated metallic spheres of $ 3\mu F $ and $ 5\mu F $ capacitances are charged to 300 V and 500V respectively. The energy loss, when they are connected by a wire is [CPMT 1999; KCET 2000; Pb. PMT 1999, 2001]

Options:

A) 0.012 J

B) 0.0218 J

C) 0.0375 J

D) 3.75 J

Show Answer

Answer:

Correct Answer: C

Solution:

$ \Delta U=\frac{1}{2}\frac{C _{1}C _{2}{{(V _{2}-V _{1})}^{2}}}{(C _{1}+C _{2})} $

$ =\frac{(3\times 5)\times {{10}^{-12}}\times {{(500-300)}^{2}}}{(3+5)\times {{10}^{-6}}} $

$ =\frac{15\times {{10}^{-12}}\times 4\times 10^{4}}{8\times {{10}^{-6}}}=0.0375J $



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