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Resistivity Question

Q5.

(a) Give an expression for the resistivity of a material in the form of a uniform wire. Define all the symbols used.

ρ = RA/L

Note that you are asked to relate resistivity to the other terms - that means say what resistivity equals in the equation.

where

ρ is resistivity,

R is the resistance

L is the length of the wire,

A is the cross-sectional area

 

(2 marks)

(b) A thin film of carbon may be used in some electronic systems. Typical dimensions of such a film are shown in the diagram.

(i) Calculate the resistance of the carbon film to a current I passing through it as shown above - resistivity of carbon = 4.0 × 10–5 Ω m

R = ρ L/A

We are used to thinking of the length of an object being 'long' but when considering resistivity the current flows parallel to the length of the object. The length doesn't have to be the longest dimension.

The current flows perpendicular to the cross sectional area of the object. The length doesn't have to have the smallest dimensions.

R = 4.0 × 10–5 x 3.0 x 10-3 / (2.0 x 10-6 x 8.0 x 10-3)

R = 7.5 Ω

(ii) Without recalculating the resistance of the carbon film, explain how you would expect the resistance to change if the current flowed as shown below.

You should consider the numerical ratio or factor by which each dimension affecting the resistance has changed.

The length has decreased a by a factor of 1500 - that will decrease the resistance by a factor of 1500.

The cross sectional area has increased by a factor of 1500 - that will decrease the resistance by a factor of 1500.

(Overall that will decrease the resistance by a factor of 1500 x 1500 = 2.25 x 106 - but you were not asked for that!)

(4 maximum marks)

(Total 6 marks)