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