A) equal to the energy finally stored in the capacitor.
B) half of the energy finally stored in the capacitor.
C) twice the energy finally stored in the capacitor.
D) 4 times the energy finally stored in the capacitor.
Correct Answer: D
Solution :
The charge on the capacitor will charge from \[-\varepsilon C\]to \[\varepsilon C\]where \[\varepsilon =emf\]of each cell. \[\therefore \]Total charge flowing through cell \[B=2\varepsilon C.\] Work done by battery \[B={{w}_{b}}=\varepsilon (2\varepsilon c)=2c{{\varepsilon }^{2}}\] Final energy stored in the capacitor\[=E=\frac{1}{2}C{{\varepsilon }^{2}}\] From Energy conservation law, we get \[{{W}_{b}}-\]Heat produced = change in the energy stored in the capacitor \[\therefore \]\[2C{{\varepsilon }^{2}}-\]heat produced \[=\frac{1}{2}C{{\varepsilon }^{2}}-\frac{1}{2}C{{\varepsilon }^{2}}=0\] \[\Rightarrow \]\[2C{{\varepsilon }^{2}}-\]Heat produced = 0 \[\Rightarrow \]Heat produced \[=2C{{\varepsilon }^{2}}\] \[\therefore \]heat produced \[=2C{{\varepsilon }^{2}}=4E\] Hence, the correction option is (d).
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