Voltage, Current and Resistance
PS
Your first exposure to the study of DC electricity has been an experiment in
which you applied various voltages to a fixed resistance and measured the
resulting current. You recorded your results in a table and transferred to Excel
to graph. You converted your readings in milliamps to amperes (amps), and
plotted V vs I where V is on the vertical axis and I is on the horizontal.
I
R
V
This arrangement goes against the convention which puts the independent variable on the x-axis, but you
will see why we do this shortly.
The point of our lab is to see how voltage and current relate to each other and to the resistance in the
circuit.
Current is defined as the “rate of flow of charge”. The charge comes from the electrons (or other charged
particles, like ions) in the conductor. When a voltage is applied to a conductor, the electrons move from
atom to atom, and it is this motion that moves charge along in the conductor. As an electron is dislodged
and moves to the next atom it may dislodge a second electron which moves on, or the first electron may
move to the next atom. This produces a “drift velocity” for electrons which is many orders of magnitude
less than rate at which charge flows which is very nearly the speed of light.
Current, with the symbol I, has units of coulomb’s per second (C/s). One coulomb (C) of charge flowing
in 1 second (s) is 1 ampere (A). The ampere is a derived unit. Coulomb is the fundamental unit of
charge. The second is the fundamental unit of time.
1A=1C/1s
Voltage is the “push” which moves the charge along in a conductor. We think of voltage as a “potential
difference” much like the difference in potential energy between two points on a vertical line in a
gravitational field. The greater an object is above the ground, the greater its potential energy. The greater
a voltage is above “electrical ground” the greater the electrical potential energy, or potential difference.
Voltage, or potential difference, with the symbol V, is measured in volts. One volt is a potential energy
(in joules) of 1 J per 1 coulomb of charge, and so voltage has units of joules per coulomb (J/C).
1V=1J/1C
We can think of resistance as “friction” which oppose the motion of charge. Resistance is a basic
property of matter except for some very special substances called superconductors which appear to have
no resistance. Superconductors must be cooled to very low temperatures to become superconducting. A
goal in material science is to develop a room temperature superconductor. Metals tend to have low
resistances and are called conductors, while nonmetals and most compounds have high resistance and are
called insulators. Strong acids and bases and many salts dissolve in water to make ions and produce
solutions which are good conductors.
Data analysis
Open an Excel spreadsheet and enter a title, the date and your names. Label three columns as I(ma), I(A)
and V. Plot your currents in milliamps in the first column. Write a formula to convert from mA to A for
the second column, and enter the voltages in the third column. This way you can simply select that last
two columns and click the chart wizard icon to begin drawing a graph. Label the x and y axes and let the
computer determine the “line of best fit” by doing its linear regression analysis (add a trendline). Be sure
to include the formula and R2 values on the graph.
Millard’s Results:
Resistor Color
Code
Start with the band
closes to the end of the
body of the resistor.
Black
Brown
Red
Orange
Yellow
Green
Blue
Violet
Gray
White
You may have been observant and recorded the color bands on your resistor. If
not, your resistor had color bands: RED-RED-RED-GOLD.
Using the color code, predict the resistance of your resistor. Compare that to the
slope of the line.
The first two color
bands tell the first two
digits. The third band
tells the number of
zeros.
A fourth band is the %
tolerance.
None
20%
silver
10%
gold
5%
Using the slope-intercept form of the straight line (y = mx + b), and assuming that
the y-intercept is close enough to zero to ignore, write an equation for V, I and R.
If you wrote: V = R x I, then you have just “discovered” Ohm’s law. Ohm’s law is singly the most
important mathematical relationship in electronics.
Ohm’s law is usually written as ….
V = IR or
I=
V
R
0
1
2
3
4
5
6
7
8
9
Ohm’s Law Problems
1. Write a brief paragraph about the origins of Ohm’s law.
2. The unit for resistance is called the ohm and is given the symbol Ω (The Greek letter omega, not a
“horseshoe”. Knowing that V = J/C and I = C/s, determine the units to which Ω is equal.
3. What is the color code for …
a. a 100 Ω resistor
b. a 3.3 kΩ resistor
c. a 5 MΩ resistor
4. Determine the resistance of the following resistors using the color code. Express your answer both in
scientific notation (if necessary) for the number of ohms and with either KΩ or MΩ (if necessary).
a. BRN-BLK-ORG
b. GRN-VIO-YEL
c. YEL-YEL-GRN
d. RED-BRN-BLK
e. VIO-RED-BRN
5. Find the current flowing through a 1000 ohm resistor with a voltage of 13.8 volts applied to it.
6. Find the resistance of a circuit in which a voltage of 25 V produces a current of 0.0045 amperes.
7. Find the voltage across a 25 kΩ resistor through which 80 mA is flowing.
8. Find the current in a lighting strike which covers 6243 feet where the voltage is 260,000 volts and the
resistance of the air is 0.003 ohms/foot.
9. Determine the resistance of a piece of wire where the voltage across the wire is 1.35 V at a current of
30.6 amps.
10. A voltage of 9.1V is applied to two electrodes in a solution of copper(II) sulfate. A current of 360 mA
is measured. What is the resistance of the solution between the two electrodes?