GATE EC 2014 Set 1 — Question 17
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Network Theory → Circuit Fundamentals & Theorems → KCL & KVL
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Question
Consider the configuration shown in the figure which is a portion of a larger electrical network
For and currents , which one of the following is TRUE?
Correct answer
(A) i₆ = 5 A
Solution
Applying Kirchhoff's Current Law (KCL) at the nodes of the triangle network:Let the nodes be (top), (bottom-left), and (bottom-right).
From the figure, the external currents are all leaving their respective nodes. The internal currents are (from to ), (from to ), and (from to ).
Alternatively, by considering the entire sub-network as a single node, the sum of all external currents must be zero:Thus, is TRUE. Option (A) is correct.
From the figure, the external currents are all leaving their respective nodes. The internal currents are (from to ), (from to ), and (from to ).
1.At node : The current enters, while and leave.
Substituting and :2.At node : The currents are all leaving.
Substituting and :3.At node : The currents enter, while leaves.
Substituting and :Alternatively, by considering the entire sub-network as a single node, the sum of all external currents must be zero:Thus, is TRUE. Option (A) is correct.
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