3.2 Investigating the electrical resistance of a wire - variation of length or diameter

Question to be answered.  What factors affect the resistance of a circuit? e.g. how does the length or thickness of a conducting device influence the current flowing i.e. what affects the resistivity of a wire.

Circuit 30 shows how to investigate the resistance of a wire

A relatively thin wire is fastened at each end onto a meter ruler marked in mm using crocodile clips.

You need an ammeter to measure the current in amps and a voltmeter to measure the p.d. across the wire in volts.

The wire is connected in series with a battery power supply, switch and ammeter to measure the current flowing through the wire in amps.

The voltmeter, to measure the p.d, is wired in parallel across the resistance wire.

Note the ammeter is always wired in series with a component, but a voltmeter is always wired in parallel across any component under investigation.

One end of the wire connected through the voltmeter is fixed (on the left), but the other end has a crocodile clip that acts as a moveable contact point to place a various distance along the resistance wire from left to right.

Close the switch to complete the circuit and begin taking readings.

Its best to open the switch between readings to minimise the risk of heating up the wire.

You vary the distance d (mm) from the left (0 mm) to a point further along to the right and take a series of pairs of p.d and current readings e.g. every 50 mm (you can work in cm, it makes no difference!).

Using Ohm's Law, you calculate the resistance in ohms from the equation R = V / I

You can then plot a graph of resistance (Ω) versus the length of the wire d (mm) - shown on the right.

You should find the graph is linear with its x,y origin at 0,0.

This means the resistance is proportional to the length of the wire.

If you don't fix the wire exactly at 0 mm, the graph should still be linear, but, the origin of the line will not be 0,0.

If you repeat the experiment with different diameter wires, you should find the gradient becomes lower, the thicker the wire.

For the same length of wire, the resistance is less the larger the diameter of the wire.

A thinner wire is more constricted creating a greater resistance against the current flow.

A good analogy is the ease with which water flows through a thin or wider diameter pipe.

If the wire doesn't heat up, the wire should behave as an ohmic conductor i.e. V = IR is consistent over a wide range of current-voltage readings.

Be able to describe the circuit and method to investigating electrical resistance of a wire by varying the wire's length or diameter of the wire.

Be able to analyse and explain the current-voltage graph for the wire including the calculations of results for ohmic conductor.

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