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Question

A circuit has a section ABC as shown in figure. If the potentials at points A, B and C are V1,V2 and V3 respectively. The potential at point O is?
941946_e48560c8df6846149402de60b33cfba9.PNG

A
V1+V2+V3
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B
[V1R1+V2R2+V3R3][1R1+1R2+1R3]1
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C
Zero
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D
[V1R1+V2R2+V3R3](R1+R2+R3)
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Solution

The correct option is A V1+V2+V3
According to kirchhoff's first rule to O
l1l2l3=0 or
l1+l2+l3=0 ...(i)
If V0 is the electric potential at O
V1,V2 and V3 be the potential at A,B and C respectively then V0V1=l1R1.
V0V2=l2R2 and V0V3=l3R3
This, l1=(V0V1R1),l2=(V0V2R2), and l3=(V0V3R3)

putting volume of l1,l2 and l3 in (I) we get
V0V1R1+V0V2R2+V0V3R3=0

or V0[1R1+1R2+1R3]V1R1+V2R2+V3R3=0

or V0=V1R1+V2R2+V3R3[1R1+1R2+1R3]1

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