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Question

Three uncharged capacitor of capacities C1,C2,C3 are connected as shown in the figure. Then, the potential at O will be :

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A
VA+VB+VDC1+C2+C3
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B
VAC1+VBC2+VDC3C1+C2+C3
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C
VAVB+VBVD+VDVAC1+C2+C3
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D
VA+VB+VDC1C2+C2C3+C3C1
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Solution

The correct option is A VAC1+VBC2+VDC3C1+C2+C3
The potential at O be the common potential of each capacitors.
thus, Q1=C1VO,Q2=C2VO and Q3=C3VO
If VA,VB and VD are given to capacitors then charges are
Q1=C1VA,Q2=C2VB and Q3=C3VD
As total charge is conserved so Q1+Q2+Q3=Q1+Q2+Q3
C1VO+C2VO+C3VO=C1VA+C2VB+C3VD
or VO=C1VA+C2VB+C3VDC1+C2+C3

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