Required Practical: Investigating Resistance

Purpose of the Practical

This practical is designed to measure the resistance of a wire and investigate how its resistance changes with length. By varying the length of the wire in a circuit and measuring the current and potential difference, you can calculate the resistance and explore the relationship between resistance and wire length.

The main aims are:

• To measure the resistance of a wire at different lengths
• To understand how resistance depends on the length of the wire
• To use electrical equipment to measure current and potential difference accurately

Resistance depends on length because a longer wire has more atoms that electrons collide with, increasing resistance.

Equipment and Setup

You will need the following equipment:

• Power supply (low voltage DC)
• Ammeter (to measure current in amperes, A)
• Voltmeter (to measure potential difference in volts, V)
• Length of wire (usually a uniform metal wire like constantan or nichrome)
• Ruler or meter stick (to measure wire length in centimetres or metres)
• Connecting wires and a crocodile clip to vary the length of wire used

The wire should be mounted on a metre ruler or board with a scale so you can accurately change the length of wire included in the circuit.

Method Procedure

Follow these steps to carry out the investigation:

1. Set up the circuit with the power supply, ammeter in series with the wire, and voltmeter in parallel across the wire section.
2. Use the crocodile clip to select a starting length of wire (e.g. 10 cm).
3. Turn on the power supply and record the current (I) from the ammeter and the potential difference (V) from the voltmeter.
4. Repeat the measurements for several different lengths of wire (e.g. 20 cm, 30 cm, 40 cm, 50 cm), moving the crocodile clip each time.
5. Record all readings systematically in a table.
6. Ensure the current is kept low to avoid heating the wire, which would affect resistance.
7. Turn off the power supply when adjusting the crocodile clip or changing the wire length to prevent overheating and for safety.

Make sure all connections are secure and the wire is straight and not tangled to get accurate length measurements.

Calculations and Analysis

Resistance ($R$) is calculated using the formula derived from Ohm’s Law:

$$R = \frac{V}{I}$$

Where:

• $V$ = potential difference across the wire (volts, V)
• $I$ = current through the wire (amperes, A)

Calculate the resistance for each length of wire using your recorded values of $V$ and $I$.

Next, plot a graph of resistance (y-axis) against wire length (x-axis). The graph should show a straight line through the origin, indicating that resistance is directly proportional to length:

$$R \propto L$$

This means doubling the length of the wire doubles the resistance.

If the graph is not a straight line through the origin, this may indicate experimental errors or issues such as contact resistance.

Consider possible sources of error such as:

• Contact resistance at the crocodile clip
• Heating of the wire increasing resistance
• Inaccurate length measurements
• Fluctuations in current or voltage readings

Learning example:

Suppose you measure a potential difference of 2.0 V and a current of 0.5 A when the wire length is 40 cm. The resistance is:

$$R = \frac{V}{I} = \frac{2.0}{0.5} = 4.0\, \Omega$$

If at 20 cm length, the potential difference is 1.0 V and current is 0.5 A, resistance is:

$$R = \frac{1.0}{0.5} = 2.0\, \Omega$$

This shows resistance doubles as length doubles, confirming the direct proportionality.