Resistivity

What factors affect the resistance of a material?

a) Length - the further electrons have to travel through material, the more collisions they will have so the higher the value of resistance.

b) Area - a bigger area means that in any 1 second more electrons will be able to travel through a piece of wire. More electrons means more current which means less resistance.

c) Material - if you swapped all the copper wire in a circuit for wood you'd notice a lot less current and a lot more resistance in the circuit. The ability of a material to resist a current is called its resistivity, ρ. Resistivity is measured in ohm-metres ( Ω m).

d) Temperature - but I cover that in my next blog'.

So:.

R ∝ l

R ∝ l/A

R ∝ ρ

These can be combined to give:

R = ρl/A

Where:.

R = resistance (Ω)

ρ = resitivity of the material (Ω m)

I = length of wire (m)

A = cross-sectional area of the wire (m2)


The formula relating resistivity (ρ) to resistance (R), cross-sectional area (A) and length (L) is:

p=RA/L

Two videos Part 1

Part 2

Material	Resistivity (ohm•meter)
Silver	1.59 x 10-8
Copper	1.7 x 10-8
Gold	2.4 x 10-8
Aluminum	2.8 x 10-8
Tungsten	5.6 x 10-8
Iron	10 x 10-8
Platinum	11 x 10-8
Lead	22 x 10-8
Nichrome	150 x 10-8
Carbon	3.5 x 10-5
Polystyrene	107 - 1011
Polyethylene	108 - 109
Glass	1010 - 1014
Hard Rubber	1013

1 Taking the resistivity of platinoid as 3.3 x 10-7 m, find the resistance of 7.0 m of platinoid wire of average diameter 0.14 cm.

2 The resistance of the ohm is very approximately that of a column of mercury 1.06 m long and of uniform cross-section of one hundredth of a cm2. Find the resistivity of mercury.

3 What length of German silver wire, diameter 0.050 cm, is needed to make a 28 resistor, if the resistivity of German silver is 2.2 x 10-7 m?

4 The maximum allowable resistance for an underwater cable is one hundredth of an ohm per metre. If the resistivity of copper is 1.54 x 10-8 m, find the least diameter of a copper cable that could be used.

5 A block of carbon, 1.0 cm by 2.0 cm by 5.0 cm, has a resistance of 0.015 between its two smaller faces. What is the resistivity of carbon?

6 A uniform strip of eureka (resistivity 5-0 x 10-7 m) has a resistance of 0.80 per metre and is 0.25 cm wide. What is its thickness?

7 A wire of uniform cross-section has a resistance of R . What would be the resistance of a similar wire, made of the same material, but twice as long and of twice the diameter?

8 A wire of uniform cross-section has a resistance of R . If it is drawn to three times the length, but the volume remains constant, what will be its resistance?

9 A simple way to make a resistor of high resistance is to draw a line with a graphite pencil across a sheet of insulating material. One such line has a resistance of 10 M and is 80 cm long. If its width is 1.8 x 10-2 cm, what is its average thickness? (Resistivity of graphite = 6.3 x l0-5 m.)


solutions in the forum under Resistivity Question solutions







aymeric