Resistivity and resistance

What affects resistance?

What we are going to find out today

• What affects resistance• What is resistivity• What affects the resistance of a

thermistor• Calibrating a thermistor• What is a superconductor

What affects resistance

The electrons (charge carriers) want to get through this straight wire,

The atoms vibrate as they are at room temperature

What shape would we want the resistor to allow the electrons to go through

Conductive putty experiment

Caution putty is carcinogenic - use gloves

It also gets everywhere – do it on top of newspaper

What shape of putty has the lowest resistance

Resistivity

Resistivity is a property of the materialIt is how well the material conducts electricity

This formula shows that the resistance will increase if p increases or the length increases.

The resistance will decrease if the area increases

Ωm

Quick questions

1) Calculate the resistance of a uniform wire of diameter 0.32 mm and length 5.0m

The resistivity of the wire = 5.0 x 10 -7 Ωm

2) Calculate the resistance of a rectangle strip of copper length 0.08m, thickness 15 mm and width 0.80mm

The resistivity of copper= 1.7 x 10 -8 Ωm

3) A wire of uniform diameter 0.28 mm and length 1.50m has a resistance of 45 Ω

Calculate

a)Its resistivityb) The length of wire that has the resistance of 1.0Ω

A = pi r2

These questions are tricky

Answers1) Calculate the resistance of a uniform wire of diameter 0.32 mm and length 5.0mThe resistivity of the wire = 5.0 x 10 -7 Ωm

R= 5.0 x 10 -7 x 5/ (pi x 0.00162)5/(pi x 0.00000256)5/8x10-6

625000R= 31 Ω

A = pi r2

2) Calculate the resistance of a rectangle strip of copper length 0.08m, thickness 15 mm and width 0.80mm The resistivity of copper= 1.7 x 10 -8 Ωm

Area = 0.015 x 0.0080A = 0.00012L = 0.08m R = 1.7 x 10 -8 x 0.08 / 0.00012R = 0.0000113R = 11 µΩ

0.08m0.80mm

15mm

r = 0.0016

Answer question 33) A wire of uniform diameter 0.28 mm and length 1.50m has a resistance of 45 Ω

Calculate

a)Its resistivityb) The length of wire that has the resistance of 1.0Ω

A = pi r2r = 0.14 mmr= 0.00014mL = 1.50mR = 45 ΩA = 6.15 x 10 -8

=45 * (6.15 x 10 -8 / 1.5)= 0.0000018=1.8x10 -6 Ωm

Thermistor

A thermistor changes resistance when the temperature changes

A resistor’s resistance will go down with temperature as the vibrating atoms (phonons) move less meaning there are less collisions with the electrons and it is easier for them to move through

Is a thermistor the same?

Measure the resistance of the thermistor at 3 temperatures

Ice water 0 degrees CelsiusRoom temperature ? ThermometorBoiling water 100 degrees Celcius

Create a voltage - current graph for all the three situations

Voltage

Current

The gradient is the resistance

Calibrate the thermistor so you could use it to measure temperature

V = IR

Semiconductor

Thermistor at T = 0K

Full of electrons

Full of holes (free space for electrons)

Thermistor above absolute zero

energy

At the hotter temperature electrons can get into the conducting band

SuperconductorsSome special material can become superconductors

The superconductor has to be cooled down to its critical temperature (Tc)

At the critical temperature the resistance fall to zero

These can be used to make low loss power lines and very good electromagnets

Resistance

Temperature (k)0

Tc

The world record Tc of 138 K