question_answer

A capacitor of 20\[8\times {{10}^{-3}}V\] capacity charged up to 500 V is connected in parallel with another capacitor of 10\[6\times {{10}^{-3}}V\] which is charged up to 200 V. Their common potential is

A)                  500 V                                   

B)                  400 V

C)                  300 V                                   

D)                  200 V

Correct Answer: B

Solution :

                Let the charges on capacitors be \[\frac{16}{5R}\] then \[\frac{16}{7R}\] Total charge       \[{{E}_{n}}\]                                 \[4{{E}_{n}}\] Let the equivalent potential be V and since capacitors are connected in parallel their equivalent capacitance is                 \[{{E}_{n}}/4\] \[2{{E}_{n}}\]     \[{{E}_{n}}/2\]                 \[\overset{0}{\mathop{A}}\,\] \[\overset{0}{\mathop{A}}\,\]  \[\overset{0}{\mathop{A}}\,\] Given, \[\overset{0}{\mathop{A}}\,\]                 \[K=\frac{1}{2}m{{v}^{2}}\] \[W=\mu ngs\] \[\mu \]                 \[\frac{1}{2}m{{v}^{2}}=\mu mgs\] Note: Capacitors are combined in parallel when we require a large capacitance to a small potential.