(i) State Ohm's law and draw V-I graph for a conductor which follows Ohm's law. Show that the slope of V-I graph gives resistance of conductor. (ii)…

The potential difference V across the ends of given metallic wire in an electric circuit is directly proportional to current I flowing through it, provided its temperature remains the same.

Slope $\displaystyle =\frac{\mathrm{BC}}{\mathrm{AC}}=\frac{\mathrm{V}}{\mathrm{I}}$

Thus, Slope = R

Consider three resistors $\displaystyle \mathrm{R}_{1}, \mathrm{R}_{2}, \mathrm{R}_{3}$ connected in series. Let V be the potential difference across the resistors and current I flows through the circuit.

Potential difference across $\displaystyle \mathrm{R}_{1}, \mathrm{R}_{2}, \mathrm{R}_{3}$ is

$\displaystyle \mathrm{V}_{1}=\mathrm{IR}_{1}, \mathrm{~V}_{2}=\mathrm{IR}_{2}, \mathrm{~V}_{3}=\mathrm{IR}_{3}$

If $\displaystyle \mathrm{R}_{\mathrm{S}}$ is equivalent resistance in series combination and I is the current through the circuit then

$\displaystyle \mathrm{V}=\mathrm{IR}_{\mathrm{S}}$

The total potential difference,

$\displaystyle \mathrm{V}=\mathrm{V}_{1}+\mathrm{V}_{2}+\mathrm{V}_{3}$

$\displaystyle \mathrm{IR}_{\mathrm{S}}=\mathrm{IR}_{1}+\mathrm{IR}_{2}+\mathrm{IR}_{3}$

$\displaystyle \mathrm{R}_{\mathrm{S}}=\mathrm{R}_{1}+\mathrm{R}_{2}+\mathrm{R}_{3}$