SP Unit 2.2

Practicals

Resistance

SP Unit 2.2 Practicals Resistance Learners should be able to demonstrate and apply their knowledge and understanding of:
1.	Investigation of the IV characteristics of the filament of a lamp and a metal wire at constant temperature
2.	Determination of the resistivity of a metal
3.	Investigation of the variation of resistance with temperature for a metal wire

SP Unit 2.2

Practicals

Resistance

Learners should be able to demonstrate and apply their knowledge and understanding of:

Investigation of the IV characteristics of the filament of a lamp and a metal wire at constant temperature

Determination of the resistivity of a metal

Investigation of the variation of resistance with temperature for a metal wire

1. Investigation of the IV Characteristics of a Lamp Filament and a Metal Wire at Constant Temperature
⇒ Objective:
To study how current (I) varies with voltage (V) in two types of conductors—a lamp filament and a metal wire—while maintaining constant temperature, and to observe how the filament’s behavior differs from that of a typical metal wire.
⇒ Theoretical Background:
Ohm’s Law: For many conductors (at constant temperature), the relationship between voltage, current, and resistance is linear:
[math]V = IR[/math]
Where R is the resistance.
Temperature Dependence:
– For a metal wire maintained at constant temperature, the IV curve should be linear.
– A lamp filament (typically tungsten) heats up significantly when current flows. Its resistance increases with temperature, making its IV curve non-linear if temperature is not controlled.
Figure 1 Investigate the filament of a lamp and a metal wire at constant temperature
⇒ Apparatus:
For Both Samples:
– DC power supply (with adjustable voltage)
– Digital multimeter or ammeter and voltmeter
– Data logger (optional) for recording I–V data
For the Metal Wire:
– The metal wire sample
– A water bath or thermostat to maintain constant temperature
For the Lamp Filament:
– A small incandescent lamp
– A method to keep the filament temperature relatively constant (for example, very short measurement intervals to minimize heating effects or a controlled environment)
Figure 2 IV characteristic of filament
⇒ Experimental Procedure:
Setup:
Metal Wire:
– Secure the metal wire in a holder and immerse it in a temperature-controlled water bath to maintain a constant temperature.
Lamp Filament:
– Mount the lamp so that its filament is accessible for connection to the power supply and measurement instruments.
Measurements:
For the Metal Wire:
– Connect the wire in series with the multimeter(s).
– Vary the applied voltage in small increments.
– Record the corresponding current at each voltage while ensuring the water bath keeps the temperature constant.
For the Lamp Filament:
– Repeat the process, but note that the filament’s temperature may change with voltage. To approximate constant temperature, keep the measurements brief or use a method to preheat the filament to a stable operating temperature.
Data Analysis:
⇒ Plotting the IV Curve:
For the metal wire, the plot of I V should yield a straight line, indicating constant resistance.
For the lamp filament, the plot may be curved, indicating a non-linear increase in resistance with increasing voltage.
⇒ Determining Resistance:
For the metal wire, determine R from the slope ([math]R = \frac{V}{I}[/math] ).
For the filament, note the change in resistance as voltage increases.
Conclusion:
Compare the behaviors: the metal wire exhibits Ohmic behavior (linear IV relationship), while the lamp filament shows non-Ohmic behavior due to temperature-induced changes in resistance.
2) Determination of the Resistivity of a Metal
⇒ Objective:
To measure the resistivity (ρ) of a metal by determining its resistance and using its dimensions.
Figure 3 Determination of the resistivity of a metal
⇒ Theoretical Background:
Resistivity Formula:
[math]R = \rho \frac{L}{A}[/math]
OR
[math]\rho = R \frac{A}{L}[/math]
Where:
– R is the resistance,
– L is the length of the wire,
– A is the cross-sectional area.
⇒ Apparatus:
– A sample of metal wire
– Micrometer or vernier caliper (for measuring diameter)
– Ruler or meter stick (for measuring length)
– DC power supply
– Voltmeter and ammeter (or a digital multimeter)
– A four-point probe setup (if available) to reduce contact resistance
⇒ Experimental Procedure:
1. Measuring Dimensions:
Length (L): Measure the total length of the wire.
Diameter (d): Measure the diameter at several points along the wire using a micrometer. Calculate the average diameter.
Cross-sectional Area (A):
[math]A = \frac{\pi d^2}{4}[/math]
2. Measuring Resistance:
Connect the wire in a circuit with the power supply and use a multimeter to measure the voltage drop across and the current through the wire.
Calculate the resistance using Ohm’s law:
[math]R = \frac{V}{I}[/math]
3. Calculating Resistivity:
Substitute R, L, and A into the resistivity formula:
[math]\rho = R \frac{A}{L}[/math]
4. Repeat and Average:
Perform multiple measurements to minimize random errors and average the resistivity value.
3. Investigation of the Variation of Resistance with Temperature for a Metal Wire
⇒ Objective:
To investigate how the electrical resistance of a metal wire changes with temperature.
⇒ Theoretical Background:
Temperature Coefficient of Resistance:
For most metals, resistance increases with temperature. The relationship can be approximated by:
[math]R = R_0 (1 + αΔT)[/math]
Where:
- [math]R_o[/math] is the initial resistance at a reference temperature,
– α is the temperature coefficient of resistance,
– ΔT is the change in temperature.
Figure 4 The variation of the resistance with temperature for a metal wire
⇒ Apparatus:
Metal wire sample
Power supply and multimeter (to measure resistance)
Temperature-controlled environment or water bath (to vary the temperature)
Thermometer or thermocouple (to measure temperature)
Insulation (if necessary)
⇒ Experimental Procedure:
Initial Setup:
Measure the initial resistance [math]R_o[/math] of the metal wire at room temperature using a multimeter.
Record the initial temperature [math]T_o[/math]
Varying Temperature:
Place the metal wire in a temperature-controlled bath.
Gradually change the temperature (for example, by heating the water bath) and allow the wire to reach thermal equilibrium at each new temperature.
Record the new resistance R at each temperature T.
Data Recording:
Note all values of resistance and corresponding temperatures.
Calculate [math]ΔT = T – T_0[/math].
Data Analysis:
Plot resistance R versus temperature T.
The graph should show an increasing trend. Use the equation:
[math]R = R_0 (1 + αΔT)[/math]
to determine α by finding the slope:
[math]\alpha = \frac{R – R_0}{R_0 \Delta T}[/math]
Compare your experimental value of α\alphaα with the literature value for the metal.
Error Analysis:
Ensure uniform heating and proper temperature measurement.
Account for any fluctuations and take repeated measurements for accuracy.
⇒ Conclusion
IV Characteristics Experiment:
Examines the relationship between voltage and current. A metal wire shows a linear IV curve (Ohmic behavior) at constant temperature, whereas a lamp filament may show non-linearity due to temperature changes.
Resistivity Determination:
Using measured dimensions (length and diameter) and resistance, the resistivity is calculated by [math]\rho = R \frac{A}{L}[/math]. Accuracy depends on precise measurements of dimensions and resistance.
Temperature Dependence of Resistance:
By measuring resistance at various temperatures, one can determine the temperature coefficient of resistance. Plotting R versus T and applying [math]R = R_0 (1 + αΔT)[/math] shows how resistance increases with temperature for metals.