The resistance $R$ of a component can be determined from its I-V graph as $R = V/I$. This is equivalent to $R = 1 / (\text{slope of the I-V graph})$ if the graph plots I on the y-axis and V on the x-axis, as shown in the image. For resistor $R_1$, the graph is a straight line passing through the origin, indicating that $R_1$ is an ohmic resistor and follows Ohm's law. Its resistance is constant. The slope of the $R_1$ line (I/ V) is constant. For resistor $R_2$, the graph is a curve. Up to voltage $V_1$, the graph is approximately linear but less steep than $R_1$. The slope of the $R_2$ curve (I/V) is smaller than the slope of the $R_1$ line in this region. Since resistance $R = 1 / (\text{slope of I-V graph})$, a smaller slope corresponds to a larger resistance. Comparing the slopes up to $V_1$: (Slope of $R_1$) > (Slope of $R_2$). Therefore, (Resistance of $R_1$)
The $I-V$ graph for two resistors, resistor 1 ($R_1$) and resistor 2 ($R_2$), are shown below : [Image of I-V graph] Which one of the following statements about these resistors is not correct?
Asked in UPSC Geoscientist 2023 · Topic: Electric Current (Ohm's Law, resistance, resistivity, and conductivity)
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Answer: D. Up to $V_1$, the resistance of $R_1$ is larger than that of $R_2$.
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