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GATE 2016 EE (EE2) – Question 34

Electric Circuits · Network solution methods: KCL, KVL, Node and Mesh analysis · 1 mark · Multiple choice

A connected network graph has 7 branches and 5 nodes. The numbers of independent KCL and KVL equations respectively are

  1. 2 and 5
  2. 5 and 2
  3. 3 and 4
  4. 4 and 3

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Show answer and explanation

Correct answer: (D) 4 and 3

Explanation

For a connected graph, only n−1 node equations are independent because summing all KCL equations gives zero. Here this is 5−1=4.

The number of independent loops is b−n+1=7−5+1=3, giving three independent KVL equations. Therefore the pair is **4 and 3, D**.

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