CP 2 - Measuring Resistivity

Question 1

what is the standard technique for measuring the resistivity of a material in the form of a wire

Answer 1

• calculate the cross-sectional area from measurements of the diameter
• then get a value for R / l using a graphical method

Question 2

how do you measure and get a value for the diameter that will be used in the calculation from a wire

Answer 2

• you measure the diameter (aka thickness) with a micrometer

- at four places along its length at different orientations

Question 3

why do you measure the diameter four times

Answer 3

to get a good average to be used in the calculation

Question 4

what is done to the wire after its diameter is measured

Answer 4

it is taped to a half meter rule

Question 5

how should you make sure the wire is taped to the ruler and why

Answer 5

• about 1cm should be protruding from the zero mark of the ruler
• so that it can easily be held on to with crocodile clips

Question 6

what would you connect the wire to

Answer 6

a circuit

Question 7

what components would the circuit contain

Answer 7

• a cell
• a voltmeter
• an ammeter

Question 8

how would the circuit be contructed

Answer 8

• the voltmeter would be connected in parallel to the wire

- and the ammeter would be in a series to measure the total current

Question 9

why is the voltmeter connected in parallel to the wire

Answer 9

• to measure the potential difference across the wire

- so that you can use V and I to calculate the resistance at different lengths

Question 10

how would the length, l, be measured

Answer 10

• a crocodile clip is placed at the beginning of the wire
• while a second clip is placed (at a measured distance from the beginning) on another point on the wire
• the distance between the clips (or the reading on the ruler) is the length

Question 11

what is actually done in this experiment

Answer 11

• the potential difference and current are recorded for a specific length of the wire connected to the circuit
• this is then used to calculate the resistance of the wire using R = V / I
• this is then repeated for varying lengths of the wire connected to the circuit by changing the distances between the clips
• a graph for R against l is then plotted

Question 12

what are the units of the resistance and length

Answer 12

• resistance is in ohms

- length is in metres

Question 13

what is the equation for resistance with resistivity and then what is the equation for resistivity

Answer 13

• R = pl / A

- so p = RA / l

Question 14

what would A equal in this equation

Answer 14

• the diameter divided by 2 to get r (d/2)
• then use the equation for the area of a circle
• so pi r^2 would be pi x (d/2 x d/2)
• to give (pi d^2) / 4

Question 15

how would a random error be shown on a graph when plotting R and l

Answer 15

• the points wouldnt perfectly align
• to give you a perfectly straight line
• instead you would have to draw a line of best fit

Question 16

why could a random error occur in this practical despite the lengths being accurate

Answer 16

• there could be variations in pressure applied by the clips when being connected to the wire
• or there could simply be inconsistencies in the wire
• either possibility would change the resistance of the wire relative to the length

Question 17

what does it mean if the line of best fit doesnt go through the origin

Answer 17

• that there is a systematic error caused by contact resistance
• due to poor contact between the clip and the wire

Question 18

why is a graphical method good in terms of bypassing errors

Answer 18

• the impact of the random errors is reduced as the line of best fit gives us a good average to work with
• and the systematic error isnt even taken into consideration when calculating the gradient by change in R over change in l