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 :

Options

A. 5 V
B. 8 V
C. 10 V
D. 12 V

Answer

C

Explanation

Let capacitance of each capacitor is C.
Then equivalent capacitance in series is

`" "1/(C.)=1/C+1/C=2/C`
`rArr" "C.=C/2`
Charge `" "Q=C.V=C/2*15" …(1)"`
When filled with dielectric
`" "C_(1)=4C, C_(2)=C`
`" "1/(C.)=1/(4C)+1/C=5/(4C)`
`rArr" "C.=(4C)/5`
Since, charge is conserved
`" "Q=C.V.=(4C)/5V." ...(2)"`
From Eqs. (1) and (2), we get
`" "C/2 times 15 =(4C)/5 times V.`
`rArr" "V.=(15 times 5)/(4 times 2)=9.4V approx 10V`