GATE EC 2016 Set 2 — Question 16
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Network Theory → Circuit Fundamentals & Theorems → Maximum Power Transfer
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Question
In the circuit shown below, is a constant voltage source and is a constant current load.
📷 Figure: Circuit diagram showing a constant voltage source in series with a resistor and a constant current load
The value of that maximizes the power absorbed by the constant current load isCorrect answer
(B) (V_S)/(2R)
Solution
To find the value of the constant current load that maximizes the power absorbed by it, we analyze the given circuit.
Step 1: Express the Voltage across the Current Load
The circuit consists of a constant voltage source in series with a resistor and a constant current load . By applying Kirchhoff's Voltage Law (KVL) around the loop, the voltage across the constant current load is given by:Step 2: Formulate the Power Absorbed by the Load
The power absorbed by the constant current load is the product of the voltage across it and the current flowing through it:Substituting the expression for into the power equation:Step 3: Maximize the Power with respect to
To find the value of that maximizes , we differentiate with respect to and set the derivative to zero:Differentiating the expression:Solving for :Step 4: Verify the Maximum Condition
We check the second derivative of with respect to :Since , the second derivative is negative (), confirming that maximizes the power absorbed by the load.Correct Option: BContinue learning with Success Tracker
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