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Question

Four unchanged capacitors C1,C2,C3 and C4 are connected as shown in the figure. The point A, B, C and D are kept at potential V1,V2,V3 and V4 respectively. Then the potential V0 at point O is


A
V1+V2+V3+V4
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B
C1V1+C2V2+C3V3+C3V4C1+C2+C3
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C
12(V1+V2+V3+V4)
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D
12C1V1+C2V2+C3V3+C3V4C1+C2+C3+C4
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Solution

The correct option is B C1V1+C2V2+C3V3+C3V4C1+C2+C3
The potential at O be the common potential of each capacitors i.e., V0
Thus,

Q1=C1V0,Q2=C2V0,Q3=C3V0 and Q4=C4V0

If V1,V2,V3 and V4 are given to capacitor then charges are

Q1=C1V1, Q2=C2V2, Q3=C3V3 and Q4=C4V4

As total charge is conserved so,

Q1+Q2+Q3+Q4=Q1+Q2+Q3+Q4C1V0+C2V0+C3V0+C4V0=C1V1+C2V2+C3V3+C4V4

V0=C1V1+C2V2+C3V3+C4V4C1+C2+C3+C4

Hence, option B is corrcet.

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