# 86-Q3: Resistivity, Using a Wheatstone Bridge¶

Time 1$$\frac{1}{2}$$ hr.

## Apparatus¶

Metre bridge & jockey; resistance wire (length $$\approx$$ $$1\text{m}$$, resistance $$\approx 2 \Omega$$ but not less); metre rule; resistors ($$0.5\Omega, 1\Omega, 2\times 2\Omega, 5\Omega, 10\Omega, 20\Omega$$); $$1.5\text{V}$$ cell; galvanometer; 4 connecting leads (3 long, 1 short); 1 sheet graph paper; micrometer.

The aim of this experiment is to determine the electrical resistivity of the wire provided. Proceed as follows:

1. Set up a slide-wire metre bridge as illustrated below where E is a cell, G is a Galvanometer, length $$l$$ of the resistance wire is connected across the right-hand gap of the bridge, and the jockey or slider J is placed at the $$50\text{cm}$$ mark.
2. With R $$= 20 \Omega$$, find the value of length $$l$$ for which the galvanometer gives zero deflection when the slider is tapped onto the $$50\text{cm}$$ mark as shown below. (2 marks)
3. Repeat the procedure in (b) for values of R equal to $$10\Omega, 5\Omega, 2\Omega, 1 \Omega, \text{ and } 0.5 \Omega$$. (8 marks) 1. Calculate and tabulate the values of $$\frac{1}{R} \text{ and } \frac{1}{l}$$ for the values of $$R$$ equal to $$20\Omega, 10\Omega, 5\Omega, 2\Omega, 1\Omega, \text{ and } 0.5\Omega$$ obtained in (b) and (c) above. (7 marks)

2. By means of the micrometer screw gauge provided, measure the diameter of the resistance wire, and hence calculate its average diameter $$d$$. (5 marks)

3. Plot a graph of $$\frac{1}{R} \text{ vs. } \frac{1}{l}$$ (whose values are recorded in i above) and determine the gradient. (12, 5 marks)

4. Determine the resistivity $$\rho$$ of the resistance wire given that:

$\frac{1}{R} = \frac{A}{\rho} \frac{1}{l} - \frac{1}{2}$

Where $$A$$ is the cross-sectional area of the resistance wire. (4, 7 marks)