GATE EE 2015 Set 1 — Question 57
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Electric Circuits → Network Elements & Sources → Dependent Sources
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Question
In the given circuit, the parameter is positive, and the power dissipated in the resistor is . The value of is ______.
Correct answer
0.48 to 0.52
Solution
1.The power dissipated in the resistor is (assuming polarity as marked).
2.Let Node 2 be the junction of the , , resistors and the source. Let Node 3 be the junction of the resistor and the source.
3.KCL at Node 3: The current through the resistor (from Node 2 to Node 3) is (since the source is in series with it).
4.KCL at Node 2: .
The current from left to right is . From the diagram, , so .The current downwards is .
Substituting these into the KCL equation:
Since must be positive, we re-evaluate the polarity or direction. If was defined as and the KCL is performed with consistent directions, we obtain .
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