question_answer

Two condensers of capacity C and 2C are connected in parallel and these are charged up to V volt. If the battery is removed and dielectric medium of constant K is put between the plates of first condenser, then the potential at each condenser is

A) \[\frac{V}{K+2}\]                     

B) \[2+\frac{K}{3V}\]

C) \[\frac{2V}{K+2}\]                   

D) \[\frac{3V}{K+2}\]

Correct Answer: D

Solution :

Initially, Equivalent capacitance of the system \[{{C}_{eq}}=3C\] Total charge \[Q =(3C)V\] Finally, Equivalent capacitance of the system \[{{C}_{eq}}\,\,=\,\,\,KC+2C\] Hence common potential \[\,V=\frac{Q}{(KC+2C)}=\frac{3CV}{(K+2)C}\,\,=\,\,\frac{3V}{K+2}\]