Required Practical: Investigating Resistance

The first investigation asks how the resistance of a wire changes with its length at constant temperature. Use a battery or suitable low-voltage power supply, an ammeter, a voltmeter, connecting leads, crocodile clips and a thin resistance wire, such as constantan or nichrome, taped alongside a metre ruler.

One crocodile clip stays at the zero end of the wire. Moving the second clip changes the length of wire included in the circuit. Only the section between the two clip contacts is being tested.

The ammeter is connected in series with the tested wire, so the current through the wire passes through it. The voltmeter is connected across the two clip contacts, so it measures the potential difference across that same section.

Set up and check the circuit with the supply switched off. Trace the current path from the supply through the ammeter and tested wire back to the supply, then check that the voltmeter spans the tested section.

1. Place the movable clip at a chosen length and measure the distance between the clip contacts using the ruler.
2. Switch on briefly and record the current and potential difference, then switch off.
3. Move the clip to test several other lengths, recording both meter readings each time.
4. Repeat measurements at each length, allowing the wire to cool before taking further readings. Calculate resistance from each pair of readings and find a mean resistance for each length.

A results table needs columns for length, potential difference, current and calculated resistance, with units in the headings: cm or m, V, A and $\Omega$ respectively.

Making length the only changing factor

The independent variable is the length between the clips. The dependent variable is the calculated resistance. Use the same wire throughout to keep its material and thickness unchanged, and keep the power-supply setting unchanged.

Temperature must also remain as constant as possible because heating changes the wire's resistance. Use a low potential difference, switch off between readings and allow the wire to cool. Short sections have low resistance, so they can carry a large current and become especially hot. Avoid touching the wire while it is powered or still hot, and switch off before moving connections.

Interpreting the resistance–length graph

Plot resistance on the vertical axis and wire length on the horizontal axis, then draw a line of best fit. For a uniform wire at constant temperature, resistance is directly proportional to length: doubling the length doubles the resistance. The expected graph is a straight line through the origin.

A longer section provides a longer conducting path, so it offers more resistance. This comparison is meaningful only when the material, thickness and temperature stay unchanged.

Real results may not pass exactly through the origin. A clip placed slightly away from the ruler's zero can introduce a length zero error. Resistance at the contacts can also contribute to the measured resistance. Check the contact positions and make secure connections rather than assuming every departure from the ideal graph is caused by the wire itself.

Comparing resistors in series and parallel

The second investigation changes the arrangement of two resistors while keeping the resistors themselves the same. Use two equal resistors, for example two $10\,\Omega$ wire-wound resistors, with a battery or suitable power supply, switch, ammeter, voltmeter, connecting leads and crocodile clips. Wire-wound resistors help reduce overheating problems.

First connect the resistors in series. The ammeter measures the current through both resistors, and the voltmeter spans the whole pair. Check the circuit against the diagram, close the switch briefly and record the readings. Calculate the total resistance using $R = V/I$.

Open the switch before reconnecting the same resistors in parallel. The ammeter must now be in the main supply path, before the current divides or after it rejoins, so it measures total current, not just one branch current. The voltmeter connects across the two points shared by both branches. Check the connections, take readings and calculate the total resistance again. Repeat measurements to check that the comparison is consistent, keeping the supply setting and resistor temperature as steady as possible.

Explaining the comparison

In series, there is one path through both resistors. Their resistances add:

$$R_{\text{total}} = R_1 + R_2$$

Two $10\,\Omega$ resistors therefore have an expected total resistance of $20\,\Omega$ in series.

In parallel, the branches provide alternative paths for current. Each resistor has the same potential difference across it, but the supply delivers current to both branches. The total resistance is lower than either individual resistance. For two equal resistors, it is half the resistance of one: two $10\,\Omega$ resistors have an expected total resistance of $5\,\Omega$ in parallel.

The measured potential difference may differ slightly between arrangements, so compare the calculated resistances rather than the current readings alone.

• Change the distance between crocodile clips on resistance wire attached to a metre ruler.
• Measure length, current and potential difference; calculate resistance for each length.
• Keep material, thickness and temperature unchanged. Use low potential difference, switch off between readings and allow cooling.
• Repeat readings and calculate means.
• Plot resistance against length: a straight line through the origin shows $R \propto L$.
• Clip-position zero error and contact resistance can affect results.

Resistor arrangements

Use the same two equal resistors in both arrangements; measure total current and potential difference across the whole pair.

• Series: $R_{\text{total}} = R_1 + R_2$.
• Parallel: total resistance is lower than either individual resistance; two equal resistors give half the resistance of one.
• Switch off before rearranging; calculate resistance separately from each pair of meter readings.