Question

The value of the voltage V1 at the node in the circuit given below is __________

(a) 11.148 V

(b) 10.989 V

(c) 20.151 V

(d) 25.148 V

The question was posed to me in class test.

This interesting question is from Advanced Problems on Superposition Theorem topic in portion Useful Theorems in Circuit Analysis of Network Theory

Answer 1

The correct choice is (a) 11.148 V

Explanation: The datum node is the lower branch.

 By superposition, the current i is given by, i = 2 \(\frac{7}{15+5+7} + \frac{3}{15+5+7} + 4I \frac{7+15}{15+5+7}\)

Or, I = \(\frac{17}{27} + \frac{88}{27I}\)

∴ The solution for i yields, I = \(\frac{\frac{17}{27}}{1 – \frac{88}{27}} = -\frac{17}{61}\) A

∴ V1 = V2 – (4I – i) 15 = 11.148 V.