Two capacitors of capacitance `C` and `nC` are connected in parallel. A battery of emf `V` is connected across the combination. Now the battery is removed and a dielectric constant K is inserted filling the space between the plates of capacitor of capacitance C. The final potential difference across the system is

Options

A. `((n+1)V)/((K+n))`
B. `(V)/(K+n)`
C. `V`
D. `(nV)/(K+n)`

Answer

A

Explanation

`Q=C_(eq)V" "Q`=Equivalent
`Q=(n+1)CV`
After intersection dielectric equivalent `C_(eq)`
`C_(eq)'=KC+nC, C_(eq)'=C(n+K)`
Conservation of charge `V=((n+1)CV)/(n(n+K)C)=((n+1)/(n+K))V`