Resistivity defines how high the resistance is for a material with unit dimensions. It is a constant for a given material.
For example, silver has a low resistivity, so silver wire will have a lower resistance than metals of the same dimensions and higher resistivity.
The resistance of a wire depends upon what material it is made of, as well as the dimensions of the wire. The property of the wire that determines this is the resitivity.
Equation
Can you rearrange the equation to make ρ the subject?
Use quizzes to practise application of theory.
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The resistivity of copper is about
Resistivity is the resistance of a 1 m cube, this would have a very low resistance.
The resistivity of glass is about
Glass is an insulator, a 1m cube would have a very high resistance.
A semiconductor has a resistivity of 10 Ωm. What is the resistance of a 1cm long cylinder with a cross sectional area of 1 mm2 ?
1cm is 0.01 m and 1 mm2 is 10-6 m2 so R = ρL/A = 10 x0.01/10-6 = 107 Ω
The picture show three cylinders of copper:
What is their order of highest to lowest resistance?
C is long and thin so is the largest resistance, B is the smallest. D is about 1/2 the length of A but the area of A is more than 2x bigger.
The picture shows two copper cylinders.
If the resistance of A is 10 mΩ, the resistance of B is:
10 mΩ is 0.01 Ω, cylinder B is half as long so has half the resistance
The picture shows two copper cylinders:
Cylinder A has resistance R.
If the radius of A is 3 times the radius of B the resistance of B is:
R = ρL/A so is inversely proportional to A. Cross section is circular so A = πr2 so R is proportional to 1/r2
The radius of B is 1/3 the radius of A so the Area is 1/9. The resistance is therefore 9R.
The picture shows two conducting cylinders.
The radius of B is 1/3 the radius of A and the resistivity of B is 3 times bigger than A.
If the resistance of A is R then the resistance of B is:
R=ρL/A =ρL/πr2
Resistance of B = 3ρL/π(1/3)2 = 27R
How much of Resistivity have you understood?
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