A) Increases by a factor of 2
B) Increases by a factor of 4
C) Decreases by a factor of 2
D) Remains the same
Correct Answer: C
Solution :
| [c] |
 |
| Charge on capacitor |
| \[q=CV\] |
| when it is connected with another uncharged capacitor. |
 |
| \[{{V}_{c}}=\frac{{{q}_{1}}+{{q}_{2}}}{{{C}_{1}}+{{C}_{2}}}=\frac{q+0}{C+C}\] |
| \[{{V}_{c}}=\frac{V}{2}\] |
| Initial energy |
| \[{{U}_{i}}=\frac{1}{2}C{{V}^{2}}\] |
| Final energy |
| \[{{U}_{f}}=\frac{1}{2}C{{\left( \frac{V}{2} \right)}^{2}}+\frac{1}{2}C{{\left( \frac{V}{2} \right)}^{2}}\] |
| \[=\frac{C{{V}^{2}}}{4}\] |
| Loss of energy \[={{U}_{i}}-{{U}_{f}}\] |
| \[=\frac{C{{V}^{2}}}{4}\] |
| i.e. decreases by a factor |
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