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B
+53V
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C
+43V
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D
−23V
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Solution
The correct option is A−53V Let the potential at point A be x
Writing the path equation relating potentials all four branches,
x−20−i1(1)=10
i1=x−30
x−15−i2(2)=20
i2=x−352
x−i3(2)−5=−50
i3=x+452
x−i4(1)=−30
i4=x+30
Applying KCL at the junction i.e at point A,
i1+i2+i3+i4=0
Applying kirchhoff current law at junciton A
(x−30)+(x−352)+(x+452)+(x+30)=0
⇒2x−60+x−35+x+45+2x+602=0
⇒6x+10=0
⇒x=−53
Thus potential at A is x=−53V
Why this question ? Tip––––: In such problems always identify the junction first, and apply KCL. Also assign the potential to unknown point and write the equation for traversing along a given path in circuit.