Question

While studying the dependence of potential difference (V) across a 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 the resistance of the resistor using this graph.

Answer 1

Ohm's law

Ohm's law states that the current through a conductor between two points is directly proportional to the voltage across the two points.

Explanation

1. The plot of potential difference (V) across a resistor versus current (I) passing through it is a straight line, that indicates that current is directly proportional to the potential difference.
2. This graph verifies Ohm's law.

Method to determine resistance

1. If the Y-axis of the graph represents voltage and X-axis represents Current then resistance is calculated as,

$\mathrm{Resistance}=\mathrm{slope}\mathrm{of}\mathrm{the}\mathrm{graph}=\frac{\mathrm{Difference}\mathrm{in}\mathrm{potential}\mathrm{difference}\mathrm{between}\mathrm{two}\mathrm{points}}{\mathrm{difference}\mathrm{in}\mathrm{current}\mathrm{between}\mathrm{two}\mathrm{points}}$

According to the graph

$$\begin{gathered} \mathrm{Resistance}=\frac{\mathrm{AB}}{\mathrm{BC}} \\ =\frac{(40-20)\mathrm{V}}{(4-2)\mathrm{A}} \\ =\frac{20}{2}\frac{\mathrm{V}}{\mathrm{A}} \\ =10\mathrm{\Omega } \end{gathered}$$