question_answer

Two identical air core capacitors are connected in series to a voltage source of 15 V. If one of the capacitors is filled with a medium of dielectric constant 4, the new potential across this capacitor is:

A)  5V                         

B)         8V

C)  10 V                     

D)         12V

E)  3V

Correct Answer: C

Solution :

Let capacitance of each capacitor is C. Then equivalent capacitance in series is \[\frac{1}{C}=\frac{1}{C}+\frac{1}{C}=\frac{2}{C}\] \[\Rightarrow \]               \[C=\frac{C}{2}\] Charge     \[Q=CV=\frac{C}{2}.15\]         ...(1) When filled with dielectric \[{{C}_{1}}=4C,{{C}_{2}}=C\] \[\frac{1}{C}=\frac{1}{4C}+\frac{1}{C}=\frac{5}{4C}\] \[\Rightarrow \]               \[C=\frac{4C}{5}\] Since, charge is conserved \[Q=CV=\frac{4C}{5}\times V\]           ...(2) From Eqs. (1) and (2), we get \[\frac{C}{2}\times 15=\frac{4C}{5}\times V\] \[\Rightarrow \]               \[V=\frac{15\times 5}{4\times 2}=9.4V\approx 10V\]