A capacitor of `20 muF` is charged to `500` volts and connected in parallel ith another capacitor of `10 muF` and charged to `200` volts. The common potential is

Options

A. 500 V
B. 300 V
C. 400 V
D. 200 V

Answer

C

Explanation

When they are joinied in parallel `C_(P)=C_(1)+C_(2)`
The total charge on the two capacitors,
`Q=Q_(1)+Q_(2)=C_(1)V_(1)+C_(2)V_(2)" "[because Q=CV]`

If V is the common potential,
then `V=(Q_(1)+Q_(2))/(C_(1)+C_(2))=(C_(1)V_(1)+C_(2)V_(2))/(C_(1)+C_(2))`
`=(20xx10^(-6)xx500+10xx10^(-6)xx200)/((20+10)xx10^(-6))`
`=(10,000+2,000)/(30)=400V`