Required Practical: Investigating Resistance

Ohm's Law states that the current through a conductor between two points is directly proportional to the voltage across the two points, provided the temperature remains constant ($V = IR$).

The resistance of a wire is determined by the collisions between moving electrons and the metal ions in the lattice. As the length of the wire increases, electrons must travel through more material, encountering more ions and thus experiencing more collisions.

Mathematically, resistance ($R$) is related to length ($L$), resistivity ($\rho$), and cross-sectional area ($A$) by the equation: $R = \rho \frac{L}{A}$

This relationship implies that a graph of Resistance ($y$-axis) against Length ($x$-axis) should result in a straight line passing through the origin, indicating direct proportionality.

Step 1: Circuit Assembly: Connect a battery or power supply in series with an ammeter, a switch, and the test wire. The test wire should be taped to a meter ruler.

Step 2: Meter Placement: Connect a voltmeter in parallel specifically across the section of the wire being tested (between the two crocodile clips).

Step 3: Data Collection: Attach the first crocodile clip at the $0$ cm mark and the second at $10$ cm. Close the switch, record the current ($I$) and potential difference ($V$), then immediately open the switch.

Step 4: Iteration: Move the second crocodile clip in increments (e.g., $10$ cm, $20$ cm, up to $100$ cm), repeating the measurements at each interval.

Step 5: Calculation: For each length, calculate resistance using $R = V/I$ and plot a graph of Resistance vs. Length.

The Origin Requirement: Always check if your graph passes through $(0,0)$. If the line is straight but has a positive y-intercept, it often indicates a zero error caused by the resistance of the crocodile clips or the contact between the clip and the wire.

Heating Effect Mitigation: Examiners frequently ask how to improve accuracy. The best answer is to turn off the power supply between readings. This prevents the wire from heating up, which would increase the resistance and cause the graph to curve.

Precision in Measurement: Use a low-voltage power supply to keep the current low. High currents lead to significant heating, which violates the 'constant temperature' requirement of Ohm's Law.

Unit Consistency: Ensure all lengths are converted to meters if calculating resistivity, though for a simple proportionality graph, centimeters are acceptable as long as they are consistent.

Parallax Error: Students often misread the position of the crocodile clip on the ruler. To avoid this, look directly down (perpendicularly) at the scale when positioning the clip.

Incorrect Voltmeter Placement: A common mistake is placing the voltmeter across the power supply instead of across the test wire. This measures the total voltage of the circuit rather than the specific potential drop across the length of wire being investigated.

Non-Linearity at High Currents: If the graph curves upwards at higher lengths/currents, it is not a failure of the principle but an indication that the wire's temperature has increased, changing its physical properties.