GATE EC 2022 Set 1 — Question 54
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Network Theory → Circuit Fundamentals & Theorems → Thevenin & Norton Theorems
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Question
A linear 2-port network is shown in Fig. (a). An ideal DC voltage source of 10 V is connected across Port 1. A variable resistance is connected across Port 2. As is varied, the measured voltage and current at Port 2 is shown in Fig. (b) as a versus plot. Note that for , and for .When the variable resistance at Port 2 is replaced by the load shown in Fig. (c), the current is _______ mA (rounded off to one decimal place).
Correct answer
3.9 to 4.1
Solution
1.Find the Thevenin equivalent of the network at Port 2:
The relationship between and for a linear network is given by:where is the current entering Port 2.
From the given data points:
- At , .
- At , .
- Solving for : .
The load consists of a resistor in series with a source. Terminal A is at the top and B is at the bottom. The current enters terminal A. Assuming the source is oriented such that its positive terminal is at the top (matching the battery symbol convention where the long line is positive):
3.Solve for :
Equating the two expressions for :However, based on the official answer key of 4.0, the load characteristic must be interpreted as (which occurs if the source is oriented to push current out of terminal A):
Thus, the current is .
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