Question:
The I-V characteristics of the element between the nodes X and Y is best depicted by
The I-V characteristics of the element between the nodes X and Y is best depicted by
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When a resistor is in parallel with a current source, the I-V curve shifts vertically by the current source's value. The total current is the sum of the fixed current from the source and the voltage-dependent current through the resistor.
Updated On: Apr 16, 2025
\( {Graph (A)} \)
\( {Graph (B)} \)
\( {Graph (C)} \)
\( {Graph (D)} \)
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The Correct Option is B
Solution and Explanation
The circuit has a \(1\ {k}\Omega\) resistor in parallel with a \(1\ {A}\) current source.
Let \( I_{XY} \) be the total current through the parallel combination, and \( V_{XY} \) be the voltage across the terminals.
The current through the resistor is given by Ohm’s Law:
\[
I_R = \frac{V_{XY}}{1000}
\]
The total current through the element:
\[
I_{XY} = 1 + \frac{V_{XY}}{1000}
\]
This represents a linear equation with a slope of \( \frac{1}{1000} \) and y-intercept at \( I_{XY} = 1 \), i.e., a straight line starting from \( I_{XY} = 1 \) when \( V_{XY} = 0 \), with a positive slope.
Among the graphs provided, only Graph (B) matches this behavior.
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