The graphs between current (I) and voltage (V) for three linear resist

The graphs between current (I) and voltage (V) for three linear resistors 1, 2 and 3 are given below :

”R₁
”R₃
This question was previously asked in
UPSC NDA-2 – 2018
The correct relationship between the resistances is R₃ > R₂ > R₁.
For a linear resistor obeying Ohm’s Law (V=IR), the relationship between current (I) and voltage (V) is linear. On a graph with Current (I) on the Y-axis and Voltage (V) on the X-axis, the slope of the line represents I/V. According to Ohm’s Law, V/I = R, so I/V = 1/R. Therefore, the slope of the I-V graph is inversely proportional to the resistance (Slope = 1/R).
A steeper slope on this I-V graph indicates a higher value of I for a given V, meaning a higher I/V ratio. Since Slope = 1/R, a higher slope corresponds to a lower resistance.
From the graph, line 1 has the steepest slope, followed by line 2, and line 3 has the shallowest slope.
Slope₁ > Slope₂ > Slope₃
Since Slope = 1/R, this implies:
1/R₁ > 1/R₂ > 1/R₃
Taking the reciprocal reverses the inequality signs:
R₁ < R₂ < R₃ Therefore, the order of resistances from largest to smallest is R₃ > R₂ > R₁.
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