question_answer

A parallel plate capacitor with air as dielectric is charged to a potential V using a battery. Removing [he battery, the charged capacitor is then connected across an identical uncharged parallel plate capacitor filled with wax of dielectric constant K. The common potential of both the capacitors is

A)  V volt                                  

B)  KV volt

C)   (K + 1) V volt                                   

D)  \[\frac{V}{K+1}\]volt

Correct Answer: D

Solution :

  Here,                     \[{{C}_{2}}=K{{C}_{1}}\]where, \[{{C}_{2}}\] is the uncharged capacitor. The value of charge on \[{{C}_{1}}\] \[Q={{C}_{1}}V\] Total capacitance \[={{C}_{1}}+{{C}_{2}}={{C}_{1}}+K{{C}_{1}}\] \[={{C}_{1}}(1+K)\] Let common potential becomes V. \[\therefore \]  \[Q=({{C}_{1}}+{{C}_{2}})V\]                 \[{{C}_{1}}V={{C}_{1}}(1+K)V\] \[\Rightarrow \]               \[V=\frac{V}{1+K}\]volt