PHYS 203 General Physics
Laboratory Session #3
Resistors and DC Circuits
Note: You will need to draw circuit schematics for this lab. Type “draw resistor circuits
online” in google and there are links to web pages that will allow you to do this.
Activity 1: Resistors Quiz
Read the following notes about Resistors in preparation for a quiz. Attach the quiz at the
end of your laboratory write-up.
What is a Resistor?
A resistor is a device that will convert electric energy (via electric current) into heat. Unlike
a capacitor, then, a resistor does NOT store energy. It consumes it at a rate of
P = IV = I 2 R =
V2
R
(1)
where the I-V relation for a resistor (known as “Ohm’s Law.”)
V = IR
(2)
has been used. Pretty much all materials have resistance, which is given by
R=
ρl
A
(3)
where l is the length of the resistor, A is the cross-sectional Area of the resistor, and ρ is
the resistivity of the resistor material. Different materials have different resistivities, and a
table showing this is in your text.
Adjustable Resistors
There are two types of adjustable resistors: the potentiometer (usally called a “pot”) and
a rheostat. Usually a potentiometer is smaller and adjustable with a small screwdriver.
Rheostats are much larger and are capable of using large currents.
What are those Pretty Colors on the Resistors?
Typically, a resistor will have 4 color bands on them which represent the resistance values
of the resistor. Each color of the “Resistor Color Code” represents a numeric value:
Pnumonic
Bad
Beer
Rots
Our
Young
Guts
But
Vodka
Goes
Well
Numeric Representation
0
1
2
3
4
5
6
7
8
9
-1
5%
10%
20%
Color
Black
Brown
Red
Orange
Yellow
Green
Blue
Violet
Gray
White
Gold (3rd band)
Gold (4th band)
Silver (4th band)
No Color (4th band)
The resistance is determined by the first three colors on the resistor via the formula
(color1)(color2) ×10color3
|
{z
N OT a product
(4)
}
Thus, a resistor with the first three colors of
red - white - blue
would have a resistance of 29 × 106 , or 29 M Ω. For resistance values of less than 10 Ω, a
gold third band is used. Thus,
brown - red - gold
would represent 12 × 10−1 , or 1.2 Ω.
Resistor values can vary greatly, and so the 4th color band represents the tolerance for
the resistor. If there is no 4th band, then one can only be assured that the resistance value
is within 20% of the value represented by the first 3 color bands.
Sometimes, a 5th color band is used to represent the Failure Rate, as shown at
http://www.testeq.com/charts/resclr.lasso
How do you Connect Resistors?
Unlike electrolytic capacitors, resistors cannot be ”connected backwards.”
Two resistors in parallel, R1 and R2 , have a net resistance of the product over the sum
of the resistances
R1 R2
(5)
R1 + R2
Two resistors in series, R1 and R2 , have a net resistance of the sum of the resistances
R1 + R2
(6)
What are Typical Resistor Values?
From several Ω to M Ω. If the resistance value is much smaller than an Ω, that resistance
value is often ignored. Of course, that’s only in comparison to other resistance values in a
given circuit. If 12 V (for example, from a car battery) is placed across 10 µΩ, then the
current (1.2 MA) and the power loss (14.4 MW) is very high - an effect which cannot be
ignored.
What is Wire Gauge?
Wire Gauge is a measurement of the diameter of a wire. This is important because the
thicker the wire, the more current it can carry. Thicker wire also represents lower resistance.
The primary downside of thicker wire is the increased cost. Note that the higher the gauge,
the LOWER the diameter:
Gauge #
4
6
8
10
12
14
16
18
20
22
Diameter at 20 degrees C (mm) Area (mm2 )
5.189
21.15
4.115
13.30
3.264
8.366
2.588
5.261
2.053
3.309
1.628
2.081
1.291
1.309
1.024
0.8235
0.8118
0.5176
0.6438
0.3255
Typically, from 10 Gauge to 14 Gauge wire is used to wire a home. 14 Gauge for lights,
12 Gauge for most other stuff, and 10 Gauge for wiring a stove (for example). Here is a pic
from the internet for wire gauge relating to house wiring:
What are Resistors Good For?
Power transfer, signal processing,... Pretty much every electrical system (including your
computer, telephone, toaster,...) have intentionally placed resistors.
Don’t Resistance Values Change with Temperature?
Absolutely. In fact your book has a table of temperature coefficents, α. However, the
resistance changes are usually small enough so that only a linear temperature coefficent is
required:
ρ = ρ0 (1 + α∆T )
(7)
The temperature coefficients reported in your text apply to a nominal temperature of 20
degrees C. For these values, the above equation may be rewritten
ρ = ρ20 (1 + α20 (T − 20degreesC))
(8)
Like capacitors, resistors have a damage threshold. If you try to put too much current
through too small a resistance, the resistor will melt. This is generally known as a “short
circuit.”
More Information about Resistors
Check out wikipedia.
Activity 2 - Resistor Color Code
Determine the resistance values and the tolerances for each of the following resistors (be sure
to use SI prefixes):
Resistor
Resistance
4700 ohm, 5% = yellow violet red, gold
1000 ohm, 5% = brown black red, gold
100 ohm, 2% = brown black brown, red
22 ohm, 1% = red red black, brown
150 ohm, 5% = ________________________
270 ohm, 5% = _______________________
3300 ohm, 5% = ________________________
10 ohm, 1% = _______________________
470 ohm, 2% = ________________________
6800 ohm, 10% = _______________________
3K3, 5% = ________________________
1K, 5% = _______________________
150 ohm, 1% = ________________________
2M9, 10% = _______________________
10M, 10% = ________________________
1 Mega Ohm, 5% = _______________________
1 ohm, 1% = ________________________
3M9, 20% = _______________________
1200 ohm, 5% = ________________________
1K2, 5% = _______________________
220 ohm, 1% = ________________________
3300 ohm, 2% = _______________________
47 ohm, 5% = ________________________
390 ohm, 5% = _______________________
3900 ohm, 2% = ________________________
100.000 ohm, 5% = _______________________
10K, 5% = ________________________
10.000 ohm, 5% = _______________________
1500 ohm, 2% = ________________________
56K, 5% = _______________________
1M, 10% = ________________________
470K, 1% = _______________________
1.8 ohm, 2% = ________________________
2.2 ohm, 1% = _______________________
2K76, 1% = ________________________
94.1K, 2% = _______________________
1
Some Quick Info
Kirchoff ’s Circuit Laws
The voltage induced in a circuit element is arranged so as to oppose the current flowing
through it.
Kirchoff’s Voltage Law (KVL) says that the voltage rises in any loop must be equal to
the voltage drops in that loop. Put another way, the net voltage gain around any loop must
be zero, or
X
Vi = 0
(9)
i
Kirchoff’s Current Law (KCL) says that the current entering any junction must be equal
to the current leaving that junction. This may be restated as ‘the net current entering any
junction must be zero’, or
X
Ii = 0
(10)
i
Protoboards
A protoboard, or breadboard, is basically a bunch of holes for you to put wire in. The
protoboard has connections at the bottom of the board as shown in the figure:
Using a Multimeter
Multimeters measure Resistance, AC Voltage, DC Current, and DC voltage. They sometimes
measure other things like transistor or diode properties. We won’t be using the latter in this
class, and I recommend you not measure current with the multimeter, either.
The numbers relate the “full scale” values. The tildes represent AC and the line over the
dots represents DC.
The Multimeters (or DMMs) use batteries. Please turn them off when you’re done or if
you won’t be using them for a while.
Activity 3 - Voltage Divider Experiment
Analysis
The following is a Voltage Divider Circuit:
V0
+
−
R1
+
R2
Vout
−
where the resistance values, R1 and R2 are known, as is the applied voltage, V0 .
Use Kirchoff’s Laws to determine
1. The Current through R1 .
2. The Current through R2 .
3. The Voltage across R1 .
4. The Voltage across R2 .
5. The Power Delivered by V0 .
6. The Power absorbed by R1 .
7. The Power absorbed by R2 .
Hint: Note that from Kirchoff’s Current Law, the current is the same in the two resistors.
Resistor Values
Pick three resistors from the box. Use the resistor color code to determine the resistance of
each of these. Measure the resistance of each of these with a multimeter, and Compare the
values. Are they within tolerance?
Experiment
Given 3 resistors, there are six ways to connect the voltage divider Circuit. Using a power
supply at 5 V, connect each of the circuits measuring the output voltage, V2 each time.
Compare your measured values with the theoretical values you calculated above.
Each person needs to connect each of the six circuits. Average the data points between
lab partners.
Activity 4: Conceptual Questions
Wilson Ch. 17, #3-18