A) 508 pJ
B) 692 pJ
C) 560 pJ
D) 600 pJ
Correct Answer: A
Solution :
[a] |
Internal energy = u |
\[\begin{align} & Q=CV\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,{{u}_{i}}=\frac{1}{2}\times 12\times {{10}^{-12}}\times 100 \\ & =12\times {{10}^{-12}}\,\times 10\,\,\,\,\,\,=600\,\times \,10-12\,\, \\ & =12\times {{10}^{-11}}\,J\,\,\,\,\,\,\,\,\,\,\,\,\,=6\times {{10}^{-10}}\,J \\ & \\ \end{align}\] |
After insertion |
\[C=KC=6.5\times 12\times {{10}^{-12}}\] |
Final energy \[{{u}_{f}}=\frac{{{Q}^{2}}}{2C'}\] |
\[\begin{align} & =\,\,\frac{12\times 12\times {{10}^{-11}}\,\times \,{{10}^{-11}}}{2\,\times \,6.5\,\times 12\times {{10}^{-12}}} \\ & \,\,\,\,\,\,\,\,\,\, \\ \end{align}\] |
So energy dissipated = \[=\,\,{{u}_{i}}\,=\,{{u}_{f}}\] |
\[\Rightarrow \text{ }508\text{ }pJ\] |
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