Ohm's Law and Resistivity

1. Unit 3 – Lesson 3Unit 3 – Lesson 3
Electrical Resistance inElectrical Resistance in
Conducting Wires & Ohm’s LawConducting Wires & Ohm’s Law
Nelson TB Reference Pages:Nelson TB Reference Pages:
523 - 526 for Ohm’s Law523 - 526 for Ohm’s Law

2. Copper, aluminum andand steel are all used as electricalare all used as electrical
conductors. Conductors allow charge to moveconductors. Conductors allow charge to move
through them but it is not the same as waterthrough them but it is not the same as water
moving through a pipe, butmoving through a pipe, but there are similarities.
Similarities between pipes and conductors:
1.1. The smaller the diameter of a (water) pipe, theThe smaller the diameter of a (water) pipe, the
_______ water that can flow through it. Similarly,_______ water that can flow through it. Similarly,
the smaller the diameter of a conductor (wire), thethe smaller the diameter of a conductor (wire), the
_______ the amount of charge that can flow_______ the amount of charge that can flow
through it. So, small diameter means greaterthrough it. So, small diameter means greater
electrical resistance.electrical resistance.
2.2. Think of all the times you used a straw. If theThink of all the times you used a straw. If the
straw was 5 times longer, it would be ________ tostraw was 5 times longer, it would be ________ to
suck up the liquid. This again is similar tosuck up the liquid. This again is similar to
electrical conductors; greater length means thereelectrical conductors; greater length means there
is greater electrical resistance to the flow ofis greater electrical resistance to the flow of
charge.charge.

3. Electrical Resistance in Conductors (No TB reference)
From point #1 on the previous page, we can write aon the previous page, we can write a
proportionality for electrical resistance which is based not onproportionality for electrical resistance which is based not on
diameter but cross-sectional area (which is usually ________diameter but cross-sectional area (which is usually ________
in shape).in shape).
R ∝ 1/A, the symbol means “proportional to”,, the symbol means “proportional to”, R is the resistanceis the resistance
andand A the cross-sectional area.the cross-sectional area.
From point #2, we have resistance proportional to Length (L):, we have resistance proportional to Length (L): R
∝ L
Putting both proportionalities together, we get:Putting both proportionalities together, we get:
R ∝ L/A.. If we want to getIf we want to get an equality, we put in an equal sign, we put in an equal sign
and a proportionality constant, which in this case is calledand a proportionality constant, which in this case is called
resistivity and represented by the Greek letterand represented by the Greek letter rho ((ρ).).
So,So, R = ρ(L/A). Units are: ρ in Ω m, L in m and A in m², and
R in Ω

4. Practical Applications of Understanding Resistance
1.1. Old style light bulbs ( incandescent ) use aOld style light bulbs ( incandescent ) use a
tungsten filament which is very thin (why?).tungsten filament which is very thin (why?).
2.2. Toaster power cords are usually very short (why?).Toaster power cords are usually very short (why?).
3.3. Power lines, used to carry high voltage (current isPower lines, used to carry high voltage (current is
what matters!) are thick (why?)what matters!) are thick (why?)
Resistivity Values (from page 624 of McGraw-Hill Text)
 Cu = 1.7 x 10 -8
Ω m
 Al = 2.7 x 10 -8
Ω m
 C = 3.5 x 10 -5
Ω m
 Glass = 10 10
to 10 14
Ω m
Glass has a high ρ value and is considered an
insulator

5. Ohm’s Law
In 1826, German physicistIn 1826, German physicist
Georg Simon Ohm didGeorg Simon Ohm did
experiments on variousexperiments on various
lengths and thicknesses oflengths and thicknesses of
(conducting) wire. For a(conducting) wire. For a
specific length andspecific length and
thickness, he measuredthickness, he measured
the currents through thethe currents through the
wire for various knownwire for various known
values of potentialvalues of potential
difference (voltage). Thedifference (voltage). The
shape of the graph ofshape of the graph of V
versus I is as shown.is as shown.
V
I
V v s I

6. The slope of the line is found by calculating V/IThe slope of the line is found by calculating V/I
since there is nosince there is no VV intercept value. The constantintercept value. The constant
slope represents the electrical resistance (slope represents the electrical resistance ( R ))
measured in ohms (measured in ohms (Ω). We usually remember). We usually remember
Ohm’s Law as:Ohm’s Law as: V = IR..
We can use Ohm’s Law (R=V/I) to define the ohm:We can use Ohm’s Law (R=V/I) to define the ohm:
11 Ω = 1 V/A
Note: Although we often apply Ohm’s Law to many
circuit problems, it does not apply to loads such
as light bulbs. Metallic conductors do obey
Ohm’s Law and do show a constant value of “R”
for various combinations of V and I.

7. Practice Problems
Nelson Textbook Ohm’s Law Questions:
Page 526 # 2-4, 9Page 526 # 2-4, 9
Page 542 # 41Page 542 # 41
Questions from McGraw-Hill Physics 11:
Academic Class to ignore these questions as this material was not taught.
1.1. What is the resistance of 250 m of aluminumWhat is the resistance of 250 m of aluminum
wire that has a diameter of 2.0 mm?wire that has a diameter of 2.0 mm?
Ans. 2.2 Ohms
2.2. A square carbon rod is 24 m long. If itsA square carbon rod is 24 m long. If its
resistance is 140resistance is 140 Ω, what is its width?
Ans. 2.4 mm