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The potential at point D is = ....... as...

The potential at point D is = ....... as shown In below figure.

(a) `(1)/(2) (V_(1)+V_(2))`
(b) `(C_(1)V_(2)+C_(2)V_(1))/(C_(1)+C_(2))`
(c) `(C_(1)V_(1)+C_(2)V_(2))/(C_(1)+C_(2))`
(d) `(C_(2)V_(1)-C_(1)V_(2))/(C_(1)+C_(2))`

A

`(1)/(2) (V_(1)+V_(2))`

B

`(C_(1)V_(2)+C_(2)V_(1))/(C_(1)+C_(2))`

C

`(C_(1)V_(1)+C_(2)V_(2))/(C_(1)+C_(2))`

D

`(C_(2)V_(1)-C_(1)V_(2))/(C_(1)+C_(2))`

Text Solution

Verified by Experts

The correct Answer is:
A, B, C
Suppose electric potential at D is V.
`:. V_(1)-V= (q)/(C_(1))` and `V-V_(2)=(q)/(C_(2))`
( both are in series )
`:. (V_(1)-V)/(V-V_(2))=(C_(2))/(C_(1))`
`:. V_(1)C_(1)-VC_(1)=VC_(2)-V_(2)C_(2)`
`:. V_(1)C_(1)=V(C_(1)+C_(2))`
`:. V= (V_(1)C_(1)+V_(2)C_(2))/(C_(1)+C_(2))`
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