Core Practical 2: Investigating Resistivity

The resistance of a uniform conductor is directly proportional to its length ($L$) and inversely proportional to its cross-sectional area ($A$).

This relationship is expressed by the fundamental formula: $R = \frac{\rho L}{A}$

To determine resistivity experimentally, the equation is rearranged into the form of a straight-line graph ($y = mx + c$), where $R$ is the dependent variable and $L$ is the independent variable.

In this linear model, the gradient ($m$) of the $R$ vs. $L$ graph represents the ratio $\frac{\rho}{A}$, allowing for the calculation of resistivity as $\rho = m \times A$.

Measuring Diameter: Use a micrometer screw gauge to measure the wire diameter at several points and orientations along its length to account for non-uniformity. Calculate the mean diameter ($d$) and then the area using $A = \frac{\pi d^2}{4}$.

Circuit Setup: Connect the test wire in series with a power supply and an ammeter. Use a voltmeter in parallel across the specific length of wire being tested.

Data Collection: Use a 'flying lead' (crocodile clip) to vary the length ($L$) of the wire in the circuit. Record the potential difference ($V$) and current ($I$) for at least 8 different lengths.

Temperature Control: To keep resistivity constant, the wire must not heat up. Switch off the power supply between readings and use a low current to minimize the heating effect.

Unit Conversion: Always convert diameter from millimetres ($mm$) to metres ($m$) before calculating the cross-sectional area to ensure the final resistivity is in $\Omega m$.

Zero Error: Check the micrometer for zero error before starting and subtract/add this value to all subsequent diameter readings to maintain accuracy.

Graph Interpretation: If the graph of $R$ vs. $L$ does not pass through the origin, it may indicate a systematic error such as contact resistance at the clips.

Precision: Ensure the voltmeter and ammeter have sufficient resolution (e.g., $0.01 V$ and $0.01 A$) to capture small changes in resistance as length varies.

Radius vs. Diameter: A frequent error is using the diameter directly in the area formula $\pi r^2$ instead of dividing by two first, or failing to use the correct formula $A = \frac{\pi d^2}{4}$.

Heating Effect: Neglecting to turn off the current between readings leads to an increase in temperature, which increases the resistance of most metals, resulting in a non-linear graph.

Parallax Error: When measuring the length of the wire against the ruler, failing to look directly over the mark can lead to inconsistent length readings.