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Question

# Three resistances are joined together to form a letter Y as shown in the figure.If the potentials of the terminals A,B and C are V1,V2 and V3 respectively, then determine the potential of the node O

A
[V1R21+V2R22+V3R23][1R1+1R2+1R3]2
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B
[V1R1+V2R2+V3R3][1R1+1R2+1R3]1
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C
[V1R1+V2R2+V3R3][R1+R2+R3]
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D
[V1R21+V2R22+V3R23][R21+R22+R23]
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Solution

## The correct option is B [V1R1+V2R2+V3R3][1R1+1R2+1R3]−1From the figure,Applying the junction rule to O, we get −I1−I2−I3=0⇒I1+I2+I3=0Now if V0 is the potential at point O, thenI1=(V0−V1)R1;I2=(V0−V2)R2 and I3=(V0−V3)R3;So substituting these values of I1,I2 and I3 in eq. (i), we getV0[1R1+1R2+1R3]−[V1R1+V2R2+V3R3]=0V0=[V1R1+V2R2+V3R3][1R1+1R2+1R3]−1

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