IIT JEE Physics (1978-2018: 41 Years) Topic-wise Complete Solutions

# Resistance Varies with Parameters of the Wire

## Objective

Qualitative study of the resistance formula $$R=\rho l/A$$.

## Introduction

The resistance of a wire depends on its length $$l$$, cross-section area $$A$$ and the resistivity $$\rho$$ of its material. With the accessibility of digital multimeters it has become very easy to measure resistance.

## Apparatus

Wires of different materials, different lengths and different diameters, a multimeter.

## Procedure

Collect wires of different materials and different diameters. Enamelled wires of different diameters are easily available. Take 1 metre of enamelled wires of various thicknesses say AWG 24, 28, 36 etc. Also take a wire of different material such as aluminium or nichrome. To be more precise, let us have three wires $$A_1$$, $$A_2$$ and $$B$$, the first two made of enamelled copper and $$B$$ of nichrome. Let $$A_1$$ be thinner than $$A_2$$, $$A_1$$ and $$B$$ have same thickness. Let each wire is of length 1 metre. Connect the two ends of $$A_1$$ to the two terminals of the multimeter. Measure its resistance. Now connect one end and middle point of the wire and measure the resistance. You can measure resistance of any length of the wire.

Now measure resistance of $$A_2$$ between the end points. Compare it with the resistance of $$A_1$$.

Finally, measure the resistance of $$B$$ between the ends. Compare it with the resistance of $$A_1$$.

## Discussion

The resistance is proportional to length. Thicker wire have lesser resistance. The resistance depends on the material (as the length and thickness are same but still the resistance of $$B$$ is much larger than the resistance of $$A$$).