Question

While studying the dependence of potential difference (V) across the resistor on the current I passing through it, in order to determine the resistance of the resistor, a student took 5 readings for different values of current and plotted a graph between V and I. He got a straight line graph passing through the origin. What does the straight line signify? Write the method of determining resistance of the resistor using this graph.

Answer 1

Hint: In this question we have been given a condition where a student plots a graph of V and I, he obtains a straight line. We have been asked the significance of the graph and he obtained it. Also, we have to determine a way to obtain the value of resistance from the same graph.

Complete answer:
It is said that a student took the reading for voltage by varying the current in a circuit. He took 5 readings and obtained a straight line as shown in the figure below.

            

Now, let the five readings of voltage for current \[{{I}_{1}},\]\[{{I}_{2}},{{I}_{3}},{{I}_{4}}\] and \[{{I}_{5}}\] be \[{{V}_{1}},{{V}_{2}},{{V}_{3}},{{V}_{4}}\] and \[{{V}_{5}}\] respectively as shown above. Now, we know that in a graph, for a straight line passing through origin means that the parameter on Y-axis is directly proportional to parameter on X-axis.
Therefore,
\[V\propto I\]
Therefore,
\[V=RI\] …………. (A)
Where R is the constant of proportionality.
Now, the above equation is of Ohm's law, where R signifies the Resistance. Therefore, the line graph signifies the Ohm's law.
Now we know that slope of line is given by the equation,
\[y=mx\] ……………… (B)
Where m is the slope of the line.
Now, equating (A) and (B)
 We can say that resistance R can be obtained by obtaining the slope of the line
Therefore,
We can say that resistance can be obtained by,
\[R=\dfrac{V}{I}\]

Note:
Resistance is the tendency of a material that resists the flow of current through a circuit. Resistance is measured in Ohms. The unit of resistance was named after a German physicist Simon Ohm who studied the relation between current, voltage and Resistance. The materials with high resistance are called insulators, whereas the materials with low resistance are known as the conductors.