Experiment to Study the Factors Affecting the Resistance of a Conducting Wire

To study the factors on which the resistance of a conducting wire depends, we can conduct an experiment that focuses on manipulating different variables and observing their effects on resistance. Here is an outline of the experiment:

Materials Required:
- Conducting wire (e.g., copper wire)
- Power supply
- Ammeter
- Voltmeter
- Rheostat or variable resistor
- Connecting wires
- Crocodile clips
- Measuring ruler
- Stopwatch

Procedure:

1. Setting up the Circuit:
- Connect the power supply to the ammeter, voltmeter, and the wire under test in series.
- Use crocodile clips to connect the wire under test to the rest of the circuit.

2. Measuring the Length of the Wire:
- Use a measuring ruler to measure the length of the wire under test.
- Record the measured length in a table.

3. Measuring the Diameter of the Wire:
- Use a micrometer or a vernier caliper to measure the diameter of the wire at multiple points.
- Take multiple measurements and calculate the average diameter.
- Record the calculated average diameter in the table.

4. Measuring the Current and Voltage:
- Adjust the rheostat or variable resistor to set a low current value (e.g., 0.2A) in the circuit.
- Note the current value shown on the ammeter and record it in the table.
- Measure the voltage across the wire using the voltmeter and record it in the table.
- Repeat the above steps for different current values (e.g., 0.4A, 0.6A, etc.) and record the corresponding voltage values.

5. Calculating Resistance:
- Use Ohm's law (R = V/I) to calculate the resistance of the wire for each current value.
- Record the calculated resistance values in the table.

6. Analysis and Observations:
- Plot a graph with the resistance values on the y-axis and the corresponding length of the wire on the x-axis.
- Observe the relationship between resistance and wire length. If the resistance increases with wire length, it indicates a direct proportionality.
- Plot a separate graph with resistance values on the y-axis and the wire's cross-sectional area (calculated from diameter) on the x-axis.
- Analyze the relationship between resistance and cross-sectional area. If the resistance decreases with increasing cross-sectional area, it indicates an inverse proportionality.

Conclusion:
Based on the experiment, we can conclude that the resistance of a conducting wire is directly proportional to its length and inversely proportional to its cross-sectional area. These observations align with the fundamental relationship described by the formula R = ρL/A, where R is resistance, ρ is resistivity, L is length, and A is cross-sectional area.