A student wishes to measure the resistivity of glass. A teacher suggests that its resistivity is of the order of 10^6 Ω m which is very large.
Resistivity ρ is defined by the equation:
ρ = RA / l
where R is resistance, A is cross-sectional area and l is the length of the material.
The student is given a number of sheets of glass of the same thickness and of different areas.
Design a laboratory experiment to determine the resistivity of glass. You should draw a diagram showing the arrangement of your equipment. In your account you should pay particular attention to
(a) the procedure to be followed,
(b) how the glass would be connected to the circuit,
(c) the measurements that would be taken,
(d) the control of variables,
(e) how the data would be analysed,
(f) any safety precautions that you would take.
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(a) Procedure:
1. Set up the circuit: Connect a power supply to a variable resistor (rheostat). Connect one terminal of the rheostat to an ammeter and then to one end of a piece of glass. Connect the other end of the glass to a voltmeter and then back to the power supply.
2. Measure the dimensions of the glass: Use a ruler or caliper to measure the length (l) and thickness (d) of the glass sheets. Record these values.
3. Select different glass sheets: Choose several glass sheets of different areas (A) but with the same thickness.
4. Set the variable resistor: Start with a high resistance value on the rheostat to ensure a low current flows initially.
5. Measure and record readings: Gradually decrease the resistance on the rheostat to increase the current passing through the glass. Take readings of the current (I) and voltage (V) across the glass for each selected sheet.
6. Repeat steps 4 and 5 for different resistance values: Vary the resistance on the rheostat to obtain a range of current values.
7. Repeat the experiment: Repeat the experiment with different glass sheets and record the corresponding current and voltage readings.
8. Calculate resistivity: For each glass sheet, calculate the resistivity using the given formula ρ = RA / l.
(b) Connecting the glass: Connect one end of the glass to the positive terminal of the power supply and the other end to the voltmeter. Ensure a secure and stable connection.
(c) Measurements:
- Measure and record the current passing through the glass using the ammeter.
- Measure and record the voltage across the glass using the voltmeter.
(d) Control of variables:
- Keep the thickness constant by using glass sheets of the same thickness.
- Ensure the length is consistent by measuring it accurately for each glass sheet.
- Control the current by adjusting the resistance on the rheostat.
(e) Data analysis:
- Plot a graph with current (I) on the y-axis and voltage (V) on the x-axis.
- Calculate the resistance (R) for each glass sheet using the formula R = V/I.
- Calculate the average resistance for each glass sheet.
- Use the formula ρ = RA / l to calculate the resistivity for each glass sheet.
- Plot a graph with resistivity (ρ) on the y-axis and cross-sectional area (A) on the x-axis.
- Determine the slope of the graph to find the resistivity of glass.
(f) Safety precautions:
- Ensure the circuit is properly grounded and all connections are secure to avoid short circuits.
- Use appropriate voltage values to avoid electrical shock.
- Handle the glass sheets carefully to avoid injury from broken glass edges.
(a) Procedure:
1. Set up the circuit with the following components: a power supply, an ammeter, a voltmeter, and the glass sheet.
2. Connect the power supply to the ammeter and voltmeter in series.
3. Place the glass sheet between two conducting plates, ensuring a good and even contact.
4. Adjust the power supply to provide a constant current through the circuit.
5. Measure the voltage across the glass sheet using the voltmeter.
6. Record the ammeter reading, voltmeter reading, and the dimensions (length and width) of the glass sheet.
7. Repeat the experiment with different glass sheets of varying thickness.
(b) Connection of the glass to the circuit:
The glass sheet should be connected in between two conducting plates, such as copper or aluminum plates, to ensure a good electrical contact. The conducting plates should be larger than the glass sheet to cover its entire surface area.
(c) Measurements to be taken:
1. Resistance (R): Use the ammeter to measure the current passing through the circuit. The resistance can be determined using Ohm's law: R = V/I, where V is the voltage across the glass sheet and I is the current passing through the circuit.
2. Cross-sectional area (A): Measure the width and length of the glass sheet using a ruler or vernier caliper to calculate the cross-sectional area (A = width x thickness).
3. Length (l): Measure the length of the glass sheet using a ruler or vernier caliper.
(d) Control of variables:
1. Use glass sheets of the same thickness but varying cross-sectional areas.
2. Keep the temperature constant during the experiment, as temperature affects resistivity.
(e) Data analysis:
1. Calculate the resistivity (ρ) using the formula ρ = RA / l, where R is the resistance, A is the cross-sectional area, and l is the length of the glass sheet.
2. Plot a graph of resistivity (ρ) against the reciprocal of the cross-sectional area (1/A). The slope of the graph will give the resistivity of the glass.
(f) Safety precautions:
1. Take care while handling glass sheets to avoid breakage or injury.
2. Ensure the circuit is properly wired and insulated to prevent electric shocks.
3. Use appropriate voltage and current levels to ensure safety.
4. Follow any additional safety guidelines provided by your teacher or institution.