Question P2.WE.1: Plan an experiment to measure the resistivity ρ of glass, wh...

Step 1 Identify the variables.
The independent variable is the thickness l of the glass.

• The independent variable is the thickness l of the glass.
• The dependent variable is the resistance R of the glass. Finding R involves measuring the p.d. across the glass and the current in the glass.
• The control variable is the area of the glass. Since this is mentioned in the question, suggest also that the temperature must be constant.

Step 2 Describe the method of data collection in logical steps.
To alter the independent variable, use glass sheets of different thickness but the same area. The thickness of each piece of glass is measured with a micrometer at several places and averaged.
The area A is required. This can be found by measuring the length and breadth of each sheet with a rule and multiplying the values together.
Draw a circuit diagram of an ammeter in series with the glass sheet and a power supply, with a voltmeter across the glass. Connections are made to the large surfaces of the glass. This can be done using aluminium foil, or metal plates as in a capacitor, which closely touch each large face of the glass sheet. Use a diagram to show how this is done 

The logical steps are then to record ammeter and voltmeter readings with one thickness of glass. 
Then repeat the readings with different thicknesses, suggesting sensible thicknesses of glass, perhaps every mm from 1 mm to 10 mm. If you are going to perform the experiment these thicknesses may be available, but if you are merely planning the experiment then you must suggest sensible values.
Step 3 Add any additional details. How can you obtain reasonable values? Think about the size and thickness of the glass to be used and whether you can detect a reasonable change in the dependent variable, the resistance. You might, for example, suggest using a sheet of glass 1 m² in area and 1 mm thick. Its resistance is then:
R = \frac{ρl}{A} = 10^{10} × 0.001 = 10^{7}  Ω
Can this be measured with ordinary laboratory apparatus? What voltages and what meters are suitable? A voltage of 10 V produces a current of 1 μA, which is measurable, but 100 V gives a current of 10 μA, which may be easier to measure but more dangerous. With glass of thickness between 1 and 10 mm the current will be 1–10 μA and so the ammeter should measure from 1 to 10 μA or up to 10 μA.
As you can see, this means that you need some idea of the size of quantities that can be measured. In this example you need to know what currents and voltages can be measured with ordinary laboratory equipment.
You may also give additional detail by describing how to attach the metal foil as contacts onto the large faces of the glass sheet with weights on top, or suggest that the glass be cleaned and dried

Step 4 State any safety points. Glass can cut a person’s skin and so gloves should be worn. If voltages above about 50 V are to be used, then use rubber gloves to avoid an electric shock or cover all exposed metal parts with insulation.
Step 5 Give your method of analysis. Remember, every derived quantity must be explained, so do not forget to state that for each thickness the voltage and current readings are used to find the resistance

with the formula R = \frac{V}{I} .
Since R = \frac{ρl}{A} , choose to plot a graph with R on the y-axis and l on the x-axis. The graph should be a straight line through the origin – a diagram may help here.
The gradient of the graph is \frac{ρ}{A}, so ρ = gradient × A.