Module 4

Module no.
4
Contents:
 The Resistance
 The Effect of Temperature on the Resistance
 Resistor Color Coding
 Work, Power, and Energy
Topic Objectives:
 To define the meaning of resistance
 To explain the effect of temperature on the resistance
of the wire
 To identify the values of resistor using color codes
 To solve problems dealing resistor color coding
 To differentiate energy from work and power
RESISTANCE = the opposition to the flow of current (charge)
opposition due to collisions and friction between free

electrons
collision and friction converts electrical energy into HEAT!
FACTORS affecting resistance of material

1. Type of material (ρ)
L_
2. Length (L) R =ρ
3. Cross sectional Area (A) A
4. Temperature of the material (T)
where:
ρ = CM Ω / ft at T = 20oC (room temp)
= resistivity constant
L = length in feet
A = area in circular mils (CM)
CIRCULAR MILS (CM)
mil = a unit of measurement for length
1 mil = 1__ inch (or 0.001inch)

1000
1000 mils = 1 inch
Circular mil vs. Square mil

By definition;
1 mil d = 1 mil
A wire with a diameter
1 mil A = 1CM of 1 mil has an area
of 1 CM.
Applying the definition to a wire having a diameter of 1 mil,
A = π d 2
= π (1) 2
= π sq. mil = 1 CM
4 4 4
Since 1 CM = π sq. mils

4
4
Therefore; 1 sq. mil = CM
π
So for a wire with a diameter of N mils,
π
A = (N)2 sq. mils
4
π
= (N)2 [ 4 CM ]
4 π
A = N2 CM since d = N or ACM = (dmils)2
Sample Problem:
1. Find the area of a wire with a diameter of 1/8 inch.
2. What is the resistance of a 100ft length of copper wire of

0.020 inch diameter at 20oC? ( ρat 20o = 10.37 CM Ω / ft )
3. An undetermined number of feet of wire have been used

with a diameter of 1/16 inch and the resistance is 0.5Ω.
What is the length of the wire? (same ρ)
4. What is the diameter of a wire in inch, with an area of

6925CM?
Temperature Effects on the Resistance of a copper wire
For good conductors, an

increase in temperature
will result in an increase in
the resistance level
R
(+) Temperature
coefficient
Temp
R
(-)Temperature
coefficient
Temp
http://www.electriccircuits.net/book,6,chapter,319,lesson,1470,thermoelectricity.aspx
Resistance Curve R
R2
R1
X
(Absolute Zero)
-273.15oC
-234.5oC 0C
o
T1 T2
(Inferred Absolute Zero)
Y
Using Similar Triangles
X Y /234.5/ + T1 /234.5/ + T2
= =
R1 R2 R1 R2
Note: Inferred absolute temp varies depending on material

Initial Temperature (Ti) of selected materials in oC
Silver - 234
Copper - 234.5
Gold - 274
Aluminum - 236
Tungsten - 204
Nickel - 147
Iron - 162
General Equation:
/Ti / + T1 /Ti / + T2
=
R1 R2
Sample Problems:
1. If the resistance of a copper wire is 50Ω at 20oC, what is its

resistance at 100oC?
2. If the resistance of a copper wire at freezing temperature is

30Ω, what is its resistance at -40 o C?
3. If the resistance of an aluminum at room temperature

(20 oC) is 100mΩ, at what temperature will it become
120mΩ?
Temperature coefficient of resistance
Example: Observe how wire temperature affect wire

resistance
http://www.allaboutcircuits.com/vol_1/chpt_12/5.html
At 20o Celsius, we get 12.5 volts across the load and a total of 1.5
volts (0.75 + 0.75) dropped across the wire resistance.
If the temperature were to rise to 35o Celsius, we could easily
determine the change of resistance for each piece of wire. Assuming
the use of copper wire (α = 0.004041) we get:
TEMPERATURE COEFFICIENTS OF RESISTANCE, AT 20 DEGREES C
Material Element/Alloy "alpha" per degree Celsius

==========================================================
Nickel -------- Element --------------- 0.005866

Iron ---------- Element --------------- 0.005671
Molybdenum ---- Element --------------- 0.004579
Tungsten ------ Element --------------- 0.004403
Aluminum ------ Element --------------- 0.004308
Copper -------- Element --------------- 0.004041
Silver -------- Element --------------- 0.003819
Platinum ------ Element --------------- 0.003729
Gold ---------- Element --------------- 0.003715
Zinc ---------- Element --------------- 0.003847
Steel* --------- Alloy ---------------- 0.003
Nichrome ------- Alloy ---------------- 0.00017
Nichrome V ----- Alloy ---------------- 0.00013
Manganin ------- Alloy ------------ +/- 0.000015
Constantan ----- Alloy --------------- -0.000074
Resistor Color Coding
Scheme
There are three types of resistor color coding. They have different
number of color bands and hence provide different information.
This is illustrated by the next table. You can calculate the value of
an unknown resistor by entering its color code in the fields below
the table.
4-band color code 5-band color code 6-band color code

2 digits, multiplier, 3 digits, multiplier, 3 digits, multiplier,
tolerance tolerance tolerance,
thermal coefficient
http://www.breakup.de/resources/resistor.html
How to read Resistor Color Codes
Black Brown Red OrangeYellow Green Blue Violet Gray White
0 1 2 3 4 5 6 7 8 9
THE MNEMONIC Tolerance%
B - Bad 0 (Black) Gold - 5%

B - Boy 1 (Brown) Silver - 10%
R - Ravish 2 (Red) No color - (20%)
O - Our 3 (Orange)
Y - Young 4 (Yellow)
G - Girls 5 (Green)
B - But 6 (Blue)
V- Violeta 7 (Violet)
G - Gave 8 (Gray)
W - Willingly 9 (White)
http://xtronics.com/kits/rcode.htm
http://users.etech.fh-hamburg.de/users/gelab/Html/Inhalte/resistor-color-code.htm
Sample Problems:
Find the resistance value in ohms and the percent

tolerance of:
a) Red, Violet, Orange, Silver
b) Brown, Black, Brown, Silver
c) Green, Blue, Green, Gold
d) Red, Violet, Gold, Silver
e) Red, Violet, Black, Gold, Red
f) Yellow, Black, Red, Black, Brown
g) Orange, Orange, Red, Orange, Green
Give the color code for each value of resistor

a) 330±5%
b) 2.2kΩ±10%
c) 100kΩ±5%
d) 5Ω±10%
WORK, POWER AND ENERGY
The Equation:
http://www.glenbrook.k12.il.us/gbssci/phys/class/energy/u5l1e.html
POWER = an indication of how much work (energy) can be
accomplished amount of time.
= rate of doing work
= product of voltage and current
1 Watt = One joule of work that is either absorbed or

delivered at a constant rate of 1 second
P = V x I
= W x Q
Q t
Power Equation:
W (Joules) (Watts, W)
P = t (sec)
ENERGY = Power that must be used over a period of time
= lost or gained by the system
Energy Equation:
W = (P) x (t) ( Watt-seconds or Joules)
Power (W) x time (hr)

Energy (kilowatt-hour, kWh) =
1000
POWER RATING OF RESISTORS

If Pin > PR
Pin
resistor will be damaged!
PR ( Excessive HEAT!)
Check whether the resistor in each circuit has possibly been
damaged.
+ ¼W
_ 100Ω _ 1W
9V 10Ω
+ 5V
(a)
(c)
+ ½ W
_ 1.5kΩ
24V
(b)
EFFICIENCY - the ratio of output to input power
Pout
η = x 100%
Pin
Sample Problems:
1. A 2Hp motor operates at an efficiency of 75%. What is the

power input in watts? If the applied voltage is 220V, what
is the input current?
2. What is the output in horsepower of a motor with an

efficiency of 80% and an input current of 8A at 120V?
3. How long can a 12-V car battery supply 40A to a starter
motor if the battery has 4x106 J of chemical energy that
can be converted to electric energy?
4. What is the operating efficiency of a fully loaded 2Hp dc

electric motor that draws 19A at 100V?

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Module no.

opposition due to collisions and friction between free

collision and friction converts electrical energy into HEAT!

FACTORS affecting resistance of material

1 mil = 1__ inch (or 0.001inch)

Circular mil vs. Square mil

Since 1 CM = π sq. mils

1. Find the area of a wire with a diameter of 1/8 inch.

2. What is the resistance of a 100ft length of copper wire of

3. An undetermined number of feet of wire have been used

4. What is the diameter of a wire in inch, with an area of

For good conductors, an

Note: Inferred absolute temp varies depending on material

1. If the resistance of a copper wire is 50Ω at 20oC, what is its

2. If the resistance of a copper wire at freezing temperature is

3. If the resistance of an aluminum at room temperature

Example: Observe how wire temperature affect wire

Material Element/Alloy "alpha" per degree Celsius

Nickel -------- Element --------------- 0.005866

4-band color code 5-band color code 6-band color code

THE MNEMONIC Tolerance%

B - Bad 0 (Black) Gold - 5%

Find the resistance value in ohms and the percent

Give the color code for each value of resistor

1 Watt = One joule of work that is either absorbed or

W = (P) x (t) ( Watt-seconds or Joules)

Power (W) x time (hr)

POWER RATING OF RESISTORS

1. A 2Hp motor operates at an efficiency of 75%. What is the

2. What is the output in horsepower of a motor with an

4. What is the operating efficiency of a fully loaded 2Hp dc

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