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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+C3The 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 Q′1=C1V1, Q′2=C2V2, Q′3=C3V3 and Q′4=C4V4 As total charge is conserved so, Q1+Q2+Q3+Q4=Q′1+Q′2+Q′3+Q′4C1V0+C2V0+C3V0+C4V0=C1V1+C2V2+C3V3+C4V4 V0=C1V1+C2V2+C3V3+C4V4C1+C2+C3+C4 Hence, option B is corrcet.

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