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The network as shown, with IS1 = 5 A, IS2 = 10 A, VAB = 120 V, and with IS1 = 10 A, IS2 = 5 A, VAB = 15 V. What is the value of k to describe IS1 = k IS2, such that VAB = 0?

The network as shown, with IS1 = 5 A, IS2 = 10 A, VAB = 120 V, and with IS1 = 10 A, IS2 = 5 A, VAB = 15 V. What is the value of k to describe IS1 = k IS2, such that VAB = 0? Correct Answer 2.5

According to superposition theorem the value of VAB will be a function of IS1 and IS2.

Therefore, VAB = xIS1 + yIS2

 For IS1 = 5 A, IS2 = 10 A, VAB = 120 V

120 = 5x + 10y    ----(1)

For IS1 = 10 A, IS2 = 5 A, VAB = 15 V

15 = 10x + 5y     ----(2)

Solving equations (1) & (2) we get x = -6 and y = 15

Thus, VAB = -6IS1 + 15IS2

Now for VAB = 0

-6IS1 + 15IS2 = 0

IS1 = 2.5 IS2

⇒ k = 2.5

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