# F2-4: Determination of the Resistivity of the Material of a Wire¶

## Apparatus¶

Metre bridge board; resistance wire board ($$R_x$$ - may include wires of several materials); galvanometer with $$100\Omega$$ protection resistor; resistor $$R_y$$ of $$10\Omega$$; $$1.5\text{V}$$ cell; switch; micrometer screw gauge; jockey (J); connecting leads (3 long, 5 short).

## Procedure¶

1. Set up the apparatus as above.
2. Close S, and place J at the $$50\text{cm}$$ mark. Move J until the galvanometer reads zero. Record the length $$\overline{AJ}$$. Open S.
3. Measure the length of $$R_x$$. Very gently lift the wire $$R_x$$ and measure its diameter in 5 different positions.
4. If there are wires of other materials, repeat procedure steps 2 and 3 for these wires.

## Observations¶

For each wire
Wire description: ________
$$\overline{AJ}=$$ ________ cm;
$$\overline{JB}=$$ ________ cm;
$$R_y =$$ ________ $$\Omega$$;
Length $$L$$ of wire R= ________ m
Diameter of wire R:
$$d_1=$$ ________ mm;
$$d_2=$$ ________ mm;
$$d_3=$$ ________ mm;
$$d_4=$$ ________ mm;
$$d_5=$$ ________ mm;
Average value of $$d =$$ ________ mm.

## Theory¶

This circuit is a Wheatstone Bridge. Thus $$\frac{\overline{AJ}}{\overline{JB}} = \frac{R_y}{R_x}$$ and $$R_x$$ can be found.

Now $$\rho$$ is the resistivity of the material of the wire, and $$\rho = \frac{R A}{L}$$. Where here $$R = R_x,$$ $$A = \big( \text{cross-sectional area of wire } R_x\big),$$ and $$L = \big(\text{length of } R_x\big)$$.

## Analysis¶

1. Use the theory to find $$\rho$$ of the material of each type of wire tested.
2. Find a table that shows the resistivity of many types of wire and try to deduce the type of material of each wire. Calculate the % error in each of your results.
3. Choose a suitable material or materials, giving reasons, for the construction of the following:
1. a fixed resistor of $$10000 \Omega$$
2. a variable resistor of $$5 \Omega$$
3. a lamp filament
4. a thermistor
5. a junction diode
6. a connecting wire
7. a long-distance power cable in a National Grid
8. a lightning conductor.