Question

A student carries out an experiment and plots the V-I graph of three samples of nichrome wire with resistance ${R_1},{R_2},{R_3}$ respectively (see in figure). Which of the following is true?
A) ${R_1} = {R_2} = {R_3}$
B) ${R_1} = {R_2} = {R_3}$
C) ${R_1} < {R_2} < {R_3}$
D) ${R_2} > {R_3} > {R_1}$

Answer 1

Hint: This question can be solved by using ohm’s law and slope determining method as more the angle with the x-axis more will be the slope .As we know slope for any graph $ = \tan \theta $
Or in other words it is ratio of Y coordinate to the X coordinate
Hence, $\tan \theta = \dfrac{y}{x}$

Complete step by step answer:
According to the question given we have information from the graph as follows:
Resistance, Angle or slope for current and potential difference
As discussed above no calculative value is given so we will proceed with slope method
Always assumes of normal temperature if not given in the question because as temperature rises Ohms law will no longer be valid




According to Ohm’s Law, $V = IR$ where v is the voltage, $I$ is the current and R is the resistance
Let’s study the graph above,
 Slope $ = \tan \theta = \dfrac{V}{I} = \dfrac{1}{R}$
(by ohm's law)
As $\alpha > \beta > \gamma $
So, $\tan \gamma > \tan \beta > \tan \alpha $
That means $\dfrac{1}{{{R_1}}} > \dfrac{1}{{{R_2}}} > \dfrac{1}{{{R_3}}}$
On reciprocating we get,
${R_3} > {R_2} > {R_1}$
So, the conclusion is more the angle lesser will be the resistance only for this graph
Hence option (C) is correct.

Note: Ohm's law is only valid for normal temperatures, at high temperatures it fails as wire develops lots of heat due to which resistance automatically increases and the uniformity in ohm's Law destroys. In that case resistance changes depending on the nature of material that is metal, non-metal and semiconductors.