A) zero
B) \[37.3\times {{10}^{-3}}\,\,\text{J}\]
C) \[722.5\times {{10}^{-3}}\]
D) \[760\times {{10}^{-3}}\,\,\text{J}\]
Correct Answer: B
Solution :
Ist case: Initial energy of smaller sphere \[=\frac{1}{2}{{C}_{1}}V_{1}^{2}=\frac{1}{2}\times 3.0\times {{10}^{-6}}\times {{(300)}^{2}}\] \[=135\times {{10}^{-3}}J\] IInd case: Initial energy of bigger sphere \[=\frac{1}{2}{{C}_{2}}V_{2}^{2}=\frac{1}{2}\times 5\times {{10}^{-6}}\times {{(500)}^{2}}\] \[=625\times {{10}^{-3}}J\] Total energy after connecting them is given by \[=\frac{1}{2}({{C}_{1}}+{{C}_{2}}){{V}^{2}}\] (where\[V=\frac{{{C}_{1}}{{V}_{1}}+{{C}_{2}}{{V}_{2}}}{{{C}_{1}}+{{C}_{2}}}\] \[=\frac{3\times {{10}^{-6}}\times 300+5\times {{10}^{-6}}\times 500}{3\times {{10}^{-6}}+5\times {{10}^{-6}}}\] \[=\frac{3400\times {{10}^{-6}}}{8\times {{10}^{-6}}}=425\,\,V)\] Now decrease in electrical energy \[=760\times {{10}^{-3}}-722.5\times {{10}^{-3}}\] \[=37.5\times {{10}^{-3}}J\]
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