Resistivity

Question 1

what is the relationship between the resistance of a length of wire and the length of it that is connected to a circuit

Answer 1

the resistance is directly proportional to the length (R dpt l)

Question 2

how has this relationship been deduced from a graph of resistance against length

Answer 2

• when the points are connected, it creates a straight line with a positive gradient
• starting from the origin

Question 3

if one wire has a diameter of 30swg (0.3150mm) and the other has one of 32swg (0.2743mm) , how would you calculate the ratio of the areas of cross-section of the two wires

Answer 3

• Area of 30 / area of 32
• 0.3150^2mm^2 / 0.2743^2mm^2 = 1.32
• since A = pi d^2 / 4

Question 4

if the 32swg wire has a resistance of 18.3 ohms for 1m length of it whereas the 30swg wire has 13.9 for the same length, how would the ratio be calculated

Answer 4

• R of 30 / R of 32
• 13.9 / 18.3 = 0.76
• = 1 / 1.32

Question 5

using those two values for the areas and lengths calculated, how could you relate that to the relationship between resistance and length that was first observed

Answer 5

• R dpt l
• since A = 1.32 and l = 1 / 1.32 for 1m length
• R dpt l / A

Question 6

why does the relationship between resistance and length make sense

Answer 6

• if the length is increased, there will be more positive ions for the electrons to collide with while theyre drifting
• this leads to more resistance as the flow of charge is slowed down, leading to the numerator, l, making a bigger value for resistance

Question 7

why does the relationship between resistance and area make sense

Answer 7

• if there is a larger cross-sectional area there will be more ‘space’ for the electrons to flow through
• this makes their drifting easier
• similar to water with a larger diameter pipe
• an if the flow of charge is easier the resistance is decreased
• meaning A, acting as the denominator, reduces the value for R

Question 8

how can the relationship between resistance, length and area be turned into a equation

Answer 8

• if R dpt l / A

- then R = constant x l / A

Question 9

what is this constant

Answer 9

• the property of the material of the wire

- called its resistivity

Question 10

how is this constant therefore written into the equation

Answer 10

• R = pl / A

- where p is rho, for resistivity

Question 11

what is the unit for resistivity and why

Answer 11

• rearrange to get p = RA / l
• R = ohms
• A - m^2
• l = m
• omh m^2 / m = ohm m
• so unit of p = ohm m

Question 12

what is resistivity

Answer 12

a property of a material that is defined by the equation R = pl / A