Each plate of a parallel plate air capacitor has area `S=5xx10^(-3) m^(2)` and the distance between the plates is `d=8.80 mm`. Plate `A` has positive charge `q_(1)= +10^(-10) C`, and plate `B` has charge `q_(2)=+2xx10^(-10) C`. A battery of emf `E=10 V` has its positive terminal connected to plate `A` and the negative terminal to plate `B`. (Given `epsilon_(0)=8.8xx10^(12) Nm^(2) C^(-2))`.
Energy supplied by the battery is.

Options

A. `10^(-9)J`
B. `5xx10^(9) J`
C. `50xx10^(-9) J`
D. `25xx10^(-9) J`

Answer

A

Explanation

(i) .
`C=(epsilon_(0)A)/d=(8.8xx10^(-12)xx5xx10^(-3))/(8.8xx10^(-3))=5xx10^(-12)F`
Charge on the plate after connection with the battery is
.
`q=CV=5xx10^(-12)xx10=50 pC`
Charge supplied by the battery is
`Deltaq=(50+50)pC=100pC`
Energy supplied by the battery is
(ii) `U_("battery")=DeltaqV=100xx10=1000 pJ`.