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GATE 2014 EC (EC1) – Question 17

Networks, Signals and Systems · Circuit Analysis · 1 mark · Multiple choice

The figure is part of a larger electrical network. For R = 1 Ω, i₁ = 2 A, i₄ = −1 A and i₅ = −4 A, which is TRUE?

Diagram for GATE 2014 EC (EC1) question 17
  1. i₆ = 5 A
  2. i₃ = −4 A
  3. The data suffice to conclude that the supposed currents are impossible.
  4. The data do not suffice to identify i₂,i₃,i₆.

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Show answer and explanation

Correct answer: (A) i₆ = 5 A

Explanation

Use the marked current directions, retaining the signs of the supplied currents. At the lower-left node i2=i1+i4=2−1=1A. At the upper node i3=i2+i5=1−4=−3A, so it actually flows opposite the arrow. At the lower-right node i6=i1−i3=2−(−3)=**5A,A**. The resistor loop also satisfies1−3+2=0.