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A –Level Physics:
Electrical Quantities:
Resistance and Resistivity
Objectives:
36. be able to derive the equations for combining resistances in
series and parallel using the principles of charge and energy
conservation, and be able to use these equations
39. be able to use the equation for resistivity
41. be able to use I = nqvA to explain the large range of
resistivities of different materials
Additional skills gained:
• Practical Planning
• Integrating GCSE content
Starter: Resistance is futile…
For the following resistor combinations, calculate the
total resistance and the voltmeter reading for each
assuming a total EMF of 24V
You
have
10mins
Conduction and Resistance
In pairs, discuss and create a definition of ‘conduction’
and ‘resistance’ and write them on a whiteboard
Resistance
quantifies how
strongly a component opposes the flow of
charge carriers (current)
Conduction
is the movement
of charged particles or propagation of
energy through a material
Conduction
A metal consists of positive metal ions with free electrons that
move with random motion as they collide with the ions.
If a source of emf is connected across a metal, the electric field
set up have a tendency to push the electrons toward the positive
end of the metal.
This ‘crawling’ motion towards the positive terminal is known as
the drift velocity
Drift Velocity (transport equation)
This time I will show
you the equation, and
you’ll tell me how it’s
derived! The diagram
to the left will help!
We consider the shape of a wire to be a cylinder, the current that is
flowing by can be calculated with the formula:
𝐼 = 𝑛𝐴𝑣𝑞
With ‘v’ being the drift velocity and ‘n’
the number density of electrons
Using the diagram to help,
prove how this equation was
derived
10m
Drift Velocity Practice
1. How fast would the drift velocity be for electrons
in a copper wire which has a diameter of 0.22mm
and carries a current of 0.50A? The number density
of electrons for copper (n) = 8.5x1028m-3
2. For an aluminium wire (at room temp) with a
diameter of 0.4mm, calculate the drift velocity when
a current of 2.2A passes through the wire. The
number density for aluminium is 18.2x1028m-3
Models
In pairs you will need to develop a model to help
explain conduction and resistance in metals.
Your explanation should include reference to at least
the following ideas:
• Movement of charge carriers
• Fixed lattice ions
• Collisions between ions and charge carriers
• Increased vibrations of fixed lattice ions with
temperature
• Evaluation of the strengths and weaknesses of
your model
Resistivity
Resistivity is similar to resistance with the exception that it’s an
inherent characteristic of the material itself, i.e.
“ a quantification of a material’s ability to resist the flow of
electric current”
So this means that it is a feature of the type of metal for example,
rather than anything to do with the dimensions of this metal in a
wire.
𝑅𝑒𝑠𝑖𝑠𝑡𝑎𝑛𝑐𝑒(Ω) =
𝑅𝑒𝑠𝑖𝑠𝑡𝑖𝑣𝑖𝑡𝑦 Ω𝑚 × 𝑆𝑎𝑚𝑝𝑙𝑒 𝑙𝑒𝑛𝑔𝑡ℎ(𝑚)
𝐶𝑟𝑜𝑠𝑠 − 𝑠𝑒𝑐𝑡𝑖𝑜𝑛𝑎𝑙 𝐴𝑟𝑒𝑎 (𝑚2
𝜌𝑙
𝑅=
𝐴
What is the resistance of a copper fuse wire (resistivity of
1.7x10-8 Ωm ) with a diameter of 0.4mm and 2cm in
length?
SILVER
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 1.54x10-8m,
find the smallest 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?
GOLD
Complete the following practice questions. Show all values before answering:
BRONZE
Differentiated Q
Independent Study
Research the following and write half a
page (each) on how they function:
• Potential Divider (Rheostat)
• Semiconductor Diode
Due: Monday 20th March