Two parallel plate capacitors of capacitance C each are connected in series with a battery of emf `epsilon`. Then, one of the capacitors is filled with a dielectric of dielectric constane K.
i. Find the change in electric field in the two capacitors, if any
ii. What amount of charge flows through the battery?
iii Find the change in the energy stored in the circuit, if any.

Options

A. `(k-1)/(2(k-1))CE`
B. `(k-1)/(2(k+1))CE`
C. `(k-2)/(k+2)CE`
D. `(K+2)/(k-2)CE`

Answer

B

Explanation

`Q=(C)/(2)E`
`C_(eq)=(C.KC)/(C+KC)=(C^(2)K)/(C(1+K))=(CK)/(1+K)`
`Q=(CK)/(1+k)E`
`Delta Q=((CK)/(1+K)-(C)/(2))E =(2CK-C(K-1))/(2(1+K))`
`=(2CK-CK-C)/(2(1+K))=(CK -C)/(2(1+K))`.