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Three uncharged capacitors of capacities...

Three uncharged capacitors of capacities `C_(1),C_(2)` and `C_(3)` are connected as shown in the figure to one another and the potentials `V_(1),V_(2)` and `V_(3)` respectively. Then the potential at `O` will be
.

A

`( V_(A) C _(1) + V _(B) C _(2) + V _(D) C _(3))/( C _(1) + C _(2) + C _(3))`

B

`(V _(1) V _(B) V _(D))/( C _(1) C _(2) + C _(2) C _(3) + C _(3) C _(1))`

C

`(V _(A) + V _(B) + V _(D))/( C _(1) +C _(2) + C _(3))`

D

`(V _(A) V _(B) + V _(B) V _(D) + V _(D) V _(A))/( C _(1) + C_(2) + C _(3))`

Text Solution

Verified by Experts

The correct Answer is:
A
`V _(A) - V _(0) = ( q )/(C _(1)) or q = (V _(A) - V_(0)) C _(1)`
`V _(B) - V _(0) = (q _(1))/( C _(2)) or q _(1) = (V _(B) - V _(0)) C _(2)`
`V _(D) - V _(0) = (q _(2))/(C _(3)) or q _(2) = (V _(D) - V _(0)) C _(3)`
`q = q _(1) + q _(2)`
`(V _(A) - V _(0)) C _(1) = (V _(B) -V _(0)) C _(2)`
`+ (V _(D) - V _(0)) C _(3)`
`therefore V _(0) = (V _(A) C _(1) + V _(B) C _(2) + V _(D) C _(3))/( C _(1) + C _(2) + C _(3))`
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