CHAPTER 1
Electric Power for Instruments
Overview of Chapter 1
Section 1.1 ! Review of Electric Potential: Before you can understand
how electrical equipment works you need a firm grasp of potential,
potential difference, grounding, and other electrical-energy definitions.
Section 1.2 ! Commercial Power: It makes sense to begin our study of
electronic instruments by studying their source of energy. The most
common source is the wall outlet connected to the commercial power grid.
Studying commercial power also allows an understanding of building
wiring and aspects of electrical safety.
Section 1.3 ! Direct Current: Electronic instruments contain transistors,
integrated circuits, microcomputers, etc. These require direct current
electricity (DC) whereas the wall outlet provides alternating current
electricity (AC). The words “direct current” can be applied to several
different situations. This section defines the various meanings of “direct
current.”
Section 1.4 ! Low-Current Low-Voltage DC Power Supplies: Most
scientific instruments require DC of very high quality (very steady voltage).
Converting the AC power from the wall outlet to good DC for the
instrument is accomplished by a “DC power supply.” Many instruments
require currents of one ampere or less at a potential difference of a few
volts. Power supplies for these instruments are the easiest DC power
supplies to build and repair. We study their design and operation in detail.
Section 1.5 ! High-Voltage or High-Current DC Power Supplies:
Some applications require much higher voltage (perhaps thousands of
volts) and other applications require many amperes of current. Power
supplies for these instruments can be very complicated compared to lowvoltage low-current supplies. We study the general principles behind these,
but we do not study the details of construction or repair. Most people
purchase these supplies rather than build them, and when one goes bad it
is common to have it repaired or replaced by the manufacturer.
Michael D. Edmiston 1977, 2001
Chapter 1 — Page 1
Section 1.1 — Potential Difference, Potential, and Ground
Most people have heard of voltage, current, and resistance. Voltage is
most likely mentioned if a person is asked to name an electrical property,
yet voltage is often the least understood of these three.
1.1.1
Voltage Misconceptions
We often hear electric current compared to water flow through a hose. In this analogy electric current is
similar to the water flow rate; the concept of voltage is similar to water pressure; electric resistance is similar
to the friction between the water and the hose. The electricity/water analogy is not bad for understanding
the Ohm’s Law relation that current equals voltage divided by resistance (I = V/R), but the analogy is rather
poor at providing the true definition of voltage (which involves energy concepts).
The author once observed a technician (with a college physics degree) working at a prestigious laboratory
on a project involving operational amplifiers. The technician went through a whole parts-drawer of
integrated circuits, perhaps 50 ICs, and declared, “can you believe it, every one of these operational
amplifiers is defective.” No, I could not believe it; indeed, none of the ICs was defective. The problem arose
because the technician did not understand voltage. The technician thought the negative sign and the ground
sign (in the circuit diagram) meant the same thing. When I explained that the circuit required two power
supplies, one producing a positive potential with respect to ground and another providing a negative potential
with respect to ground, the response was, “what are you talking about?”
The type of misunderstanding described above is common. To prevent it you need a better understanding
of voltage than “voltage is like pressure.” In fact, the word voltage is somewhat colloquial. The formal
wording would be potential or potential difference. The definition of potential difference (voltage) requires
a review of potential-energy concepts.
1.1.2
Review of Potential Energy
Potential energy (U) is energy that depends upon position. The formal definition is made through the workenergy theorem by equating a change in potential energy ()U) to the work released when an object
undergoes a change in position:
2
∆U = w = − ∫1 F ⋅ dl
This is a line integral in which a force (F) acts on an object as the object moves along a line (l) consisting
of many small steps (dl).
When dealing with work we must distinguish whether the work equation is describing work done by us
(people) or work done by some natural force (such as gravity). When people do work on an object it gains
some type of energy. When gravity does work on an object the object loses gravitational potential energy.
The equation above assumed a natural force and this explains the negative sign. For example, if the force
(F) is gravity pulling downward and the movement (dl) is upward the object gains potential energy ()U must
be positive). But when the force is opposite the motion the vector dot product (F @ dl) produces a negative
result. Therefore the explicit negative sign in the equation makes )U positive when the line integral is
negative.
Michael D. Edmiston 1977, 2001
Chapter 1 — Page 2
If the force and motion are exactly opposite, and if the force has constant magnitude, the integral has the very
simple result:
2
∆U = w = − ∫1 F ⋅ dl = − F∆ l
If the force is gravity then F = mg and the change in position is a change in height ()h). This yields:
∆U G = − m g ∆ h
If the force is created by an electric field (E) acting on a charge (q) then we have:
2
∆U E = − ∫1 qE ⋅ dl
sometimes
=
− q E ∆x
In this case the simplification of the integral to –qE)x is not as often correct as the simplification for the
gravitational case. For gravity a change in height )h is logically assumed to be in the vertical plane which
is in-line with gravity. And for experiments near the surface of the earth gravity is fairly constant. However,
when dealing with electric fields there is no guarantee that )x is aligned with the field, and there is no
guarantee the electric field is constant; the electric field could easily vary in magnitude or direction or both.
Perhaps the word “sometimes” in the equation above should be written as “occasionally.”
1.1.3
Potential Difference
We can maintain a simple result for electric potential energy change by defining potential difference ()V).
The concept of potential difference combines the electric field and the displacement into one term:
The left equation defines )V as a property of the space. The locations of points one and two combined with
2
∆V21 = − ∫1 E ⋅ dl
 yielding

→
always
∆U 21 = q ∆V21
the electric field properties in that region of space jointly define )V. The only difference between )V and
)U is the amount of charge that moves through the space. Charge is not part of )V; charge is part of )U.
If we know the potential difference between points one and two we can calculate the energy gained by a
charge when it moves between the two points. If )V21 is +3 volts and a charge of +4 coulombs moves from
point one to point two, the charge gains 12 joules of potential energy. We have to expend 12 joules of work
to accomplish the move.
A voltmeter measures potential difference. One way for a voltmeter to work is to allow a small amount of
charge to move between the points where the probes are attached. The energy lost by the moving charge is
used to move the needle of the voltmeter. When the potential difference is large, more energy is lost and the
needle moves farther.
Michael D. Edmiston 1977, 2001
Chapter 1 — Page 3
1.1.4
Using a Voltmeter
A voltmeter has two probes: one colored black and
one colored red. To measure the potential difference
symbolized as )V21 you must connect the red probe
to point two and the black probe to point one.
Reversal of the probes will measure )V12 which has
the same magnitude but opposite sign as )V21 .
A properly-wired voltmeter will give a positive
potential-difference reading if the red probe is at the
location in space where a positive charge has higher
potential energy compared to the location of the
black probe.
∆
∆
Figure 1.1 A charge moved from point one to
point two undergoes a potential energy change of
)U21 = q)V21. The left voltmeter hook-up is the
proper way to measure )V21.
The best way is to verbalize )V21 would simply be to
say: delta V two one. This has the virtue of being
unambiguous, but it doesn’t use the words we
normally associate with )V. We might properly say: the potential difference starting at point one and
ending at point two. The following phrase using the word “between” is commonly used, but it creates
ambiguity as to which point gets the black voltmeter probe and which gets the red probe: the potential
difference between points one and two. Avoid this wording unless you are interested in magnitude only.
The rationale for writing )V21 when we start at location one and end at location two will become more
apparent in the next section about electric potential.
1.1.5
Electric Potential
Thus far we have not made any definition of electric potential; we have only defined potential difference.
Mathematically we assume the symbol )V21 means V2 – V1. If this is also true for the real world it implies
there is a physical property called electric potential. On one hand it seems easy to define electric potential.
If a potential difference exists between points one and two defined as
2 ∆V21 = − ∫ E ⋅ dl
1
this implies we can rewrite the equation as:
2
V2 − V1 = − ∫1 E ⋅ dl
2
 yielding

→ V2 = − ∫1 E ⋅ dl + V1
This makes mathematical sense, but it may not make physical sense. Our voltmeters, working on energy
principles, can measure differences in potential; we have no technique to measure an absolute potential. We
can calculate or measure the potential at location two only if we already know the potential at location one.
Another way to describe the problem is to say we have no reference point; or perhaps a better statement is
we have no obvious place where the potential is clearly zero.
This is similar to asking how much gravitational potential energy a mass possesses when it is held a few feet
above a table in the physics lab. Do we measure the height from the table, from the floor, from sea level, or
from the center of the earth? If the mass is simply going to fall onto the table, the potential energy it loses
during its fall is calculated by using the original height above the table. But if the mass is going to drop on
the table, roll across the surface and fall on the floor, the total energy lost would have to be calculated by
Michael D. Edmiston 1977, 2001
Chapter 1 — Page 4
measuring its initial height from the floor instead of from the table. But then, what happens if it falls into
a hole in the floor? Should the original height be measured from the lowest point in the lab? The question
really is, at what point does a mass have zero gravitational potential energy? In electricity we have the very
same type of question: at what point does a charge have zero electrical potential energy; and therefore, where
in space is a place that has zero electric potential?
1.1.6
Grounding: Zero Potential
Although there is no fundamental zero location for electric potential, we find it useful to pretend there is.
By agreement, the soil of the earth is defined as zero potential. The earth is slightly conductive so it is
possible to make an electrical connection to it. We pound a half-inch diameter metal rod (usually copper)
eight to ten feet into the earth and declare that rod to be at zero potential. We call this a ground rod. Any
building which uses electric power should have at least one ground rod. The ground rod is usually located
where the electric power enters the building. In some cases the building's metal water pipes are used as the
ground rod. There are some good reasons not to do this and it does not meet wiring codes in some states or
cities. An obvious problem of using plumbing for the ground connection is that some plumbing is plastic;
there may be mixed metal and plastic plumbing in a building.
As winds and clouds (especially thunderclouds) pass overhead, friction can cause charge separation between
the air and the earth. When this happens the potential of the ground rod at one building can have a vastly
different potential than those at other buildings. When we wire an instrument in one building to an
instrument in another building this can cause serious problems. For example, assume a computer in one
building and a second computer in a different building are going to be networked together by running a cable
between the buildings. If these two buildings have different ground potentials then the potential difference
causes unwanted currents on the network cables. This is one reason for using fiber-optic cable for signal
transmission between buildings. (Another benefit of fiber-optic cable is increased speed of transmission and
a higher capability of multiple transmissions sharing the same cable.)
Unless we are specifically dealing with building-to-building signal wiring, we will ignore the fact that ground
at one building might be a different potential than ground at another building. We will always consider the
ground rod has a potential of zero volts.
With zero potential defined, we can now use a voltmeter to measure potentials. We connect the black probe
of the voltmeter to the ground rod, and we place the red probe at the location where we desire the potential.
The voltmeter measures the potential difference between ground potential and the place of interest. When
the black voltmeter probe is attached to the ground rod (location one) and the red probe is at location two:
V2 = )V21 + V1 = )V21 + 0 = )V21 = (voltmeter reading)
We can now see the reasoning for the ordering of the subscripts. )V21 is the potential at location two minus
the potential at location one. Location two is the place of interest so that subscript appears closest to our
symbol V. Location one is just the reference position and it occupies the second subscript position. This
ordering of subscripts is the most common, but some people reverse the subscripts. When communicating
with a new person or when reading a new book, be sure to establish whether )V21 means V2 – V1 or the
reverse.
Michael D. Edmiston 1977, 2001
Chapter 1 — Page 5
1.1.7
Positive and Negative
When it requires positive1 work to move a positive2 charge from the ground rod (zero potential) to some other
object, that other object is at greater potential than zero. We say this object is at positive3 potential. If the
moved charge is two coulombs and the work required is ten joules the potential of this object is positive4 five
volts.
In the previous paragraph the word “positive” appears four times. Three of these (positive1, positive3, and
positive4) refer to the arithmetic sign we place before a numeric value. The remaining (positive2) identifies
which of three possible charge states we moved (positive, negative, neutral). When speaking of charge,
positive and negative and neutral are names as opposed to arithmetic signs. Benjamin Franklin might have
suggested we name one charge type red, the opposite blue, and neutral could be white. If this had been
adopted we would change positive2 to the word red. The other three occurrences of positive would continue
to be the word positive.
Now we discuss yet another meaning for positive and negative. A power source (such as a battery) has two
terminals connected to the device it powers. One of these terminals is labeled positive (+) and the other is
labeled negative (–). This use of positive could be subscripted as positive5 because it is not the same as any
of the uses of positive in the first paragraph of this section.
On a power supply, the positive and negative notations simply tell us which terminal is at higher potential
(or which is at lower potential) when compared to each other (not compared to ground). For this purpose
they could have been labeled H and L for higher and lower. If we do not realize that positive5 (on power
supplies) is different than positive3 (specifically making a comparison to ground), we might imagine the (+)
terminal of a power supply is at positive absolute potential (higher than ground). This is just as likely false
as true.
Unless a power supply is in some way connected to the ground rod, the absolute potentials of the terminals
are unknown. Take a 1.5-volt flashlight battery and examine the markings. You should find markings
indicating a 1.5-volt battery, and you should find (+) and (–) markings near the terminals at opposite ends.
Consider the (+) end. Does this terminal have an absolute potential of +1.5 volts? I have no idea, but
probably not. Its absolute potential might be +6.8 volts or +132 volts or +4917 volts. The absolute potential
of the (+) terminal does not even have to be positive; it could be –83 volts.
But we do know the following: if the (+) terminal of a 1.5-volt battery has an absolute potential (compared
to ground) of +6.8 volts, then the (–) terminal is +5.3 volts (i.e. 1.5 volts lower). If the (+) terminal is +132
volts, the (–) terminal is +130.5 volts; if (+) is +4917 then (–) is +4915.5 volts; if (+) is –83 then (–) is –84.5
volts.
Major point: unless a power supply is connected to the ground rod and you understand how that connection
is made, do not assume the (+) and (–) terminal markings of a power supply have anything to do with
absolute potentials. All you are sure they mean is that the (+) terminal is at higher potential than the (–)
terminal.
1.1.8
Current Flow
Remember that current flow is traditionally assumed as movement of positive charges. Remember the true
“charge carriers” may be positive or negative or both depending upon the conductive substance. For most
electronics projects the truth about what is “moving” just doesn’t matter. However, when analyzing circuits
and circuit diagrams it is often helpful to trace the current through the circuit. Although some people persist
Michael D. Edmiston 1977, 2001
Chapter 1 — Page 6
at thinking of electron current, and therefore perform current tracing while thinking of negative current, most
of the world (including this author) think in terms of positive current. Therefore, if you haven’t already
adopted the view that electricity is the flow of positive charges, it might be wise to adopt that view at this
time.
By thinking of current flow, there is another way to explain the
meaning of the (+) and (–) terminals of a power supply. The (+)
terminal is where the current leaves the power supply and heads
to the device being powered. The (–) terminal is where the
current reenters the power supply after it has gone through the
device.
This is totally consistent with the earlier description of (+) and
(–) as long as the power supply is actually providing energy to
the attached device. Positive charge leaves the terminal with the
higher potential and returns to the terminal with the lower
potential. By doing so the charge has lost potential energy. The
powered device receives that energy and uses it to provide
whatever service or function the device is supposed to provide.
If the device is a light bulb, the energy lost by the positive charge
flowing from (+) to (–) shows up as heat and light.
Figure 1.2 A flashlight battery
providing energy to a light bulb.
Traditional positive current flows as
indicated.
Positive charge moving from the positive terminal of a power supply, doing work in the device it travels
through, and returning to the power supply at the negative terminal is equivalent to water leaving a river at
the top of a water fall, passing through a turbine to do work for us, and returning to the river at the bottom
of the waterfall.
We now have two nearly equivalent ways to view the meaning of the positive and negative signs on a power
supply. (1) The positive terminal is the one with the higher potential. (2) The positive terminal is where the
positive current leaves the power supply. Meaning one is always correct. Meaning two is correct if the
power supply is actually providing energy. If the “power supply” is a rechargeable battery, the current
actually flows the opposite way during recharging. Since statement two is sometimes wrong, we might drop
the discussion at this point and just declare statement one as better. However, it is often helpful to relate
voltmeter readings to current flow. To do this we need a bit more time with statement two.
Electronic circuits can be composed of many parts. Some parts supply energy to other parts, and some parts
use energy received from other parts. Any device that has current flowing through it will have a potential
difference across it. That means we can put a voltmeter across the device (the red probe on one side and the
black probe on the other) and obtain a non-zero reading. With a non-zero reading it is clear the device could
be labeled with a (+) and a (–). Obviously we should put the (+) sign on the end with the higher potential.
This means put the (+) sign on the end with the red voltmeter probe if the voltmeter reading is positive. Put
the (+) sign on the end with the black voltmeter probe if the voltmeter reading is negative.
Having labeled the device with (+) and (–) as described, which way is the current going? We can answer
this question if we know whether the device is providing energy or consuming energy. If the device is
providing energy, the positive current is coming out of the (+) side. If the device is consuming energy the
positive current is coming out of the (–) side.
Whether the device is providing or consuming energy is easy to know if the device is a resistor because
resistors always consume energy from the circuit (and release that energy as heat). If the device is an
Michael D. Edmiston 1977, 2001
Chapter 1 — Page 7
electronic power supply (with transistors and/or integrated circuits) it always provides energy (otherwise it
could be destroyed). However, if the device is a battery it could be providing energy (normal) or consuming
energy (recharging). If the device is a capacitor, it could be charging or discharging. If the device is a
motor/generator it could be consuming energy (motor) or supplying energy (generator).
Figure-1.3 helps show these possibilities.
In this figure the common circuit symbols
for battery, capacitor, resistor, motor, and
generator are used. It is also common to
use a battery symbol for an electronic
power supply. In the top row, the devices
are providing energy. In the bottom row
the devices are consuming energy.
Batteries (if rechargeable), capacitors, and
motor/generators can do either. Electronic
power supplies only provide energy;
resistors only consume energy.
1.1.9
Grounding a Power Supply
Figure 1.3 Current flow can be determined from potential
difference readings if it is known whether the device is
consuming energy or providing energy to the rest of the
circuit. Resistors cannot supply energy to the circuit, and it
is assumed transistorized energy supplies cannot consume
energy from the circuit.
As mentioned earlier, if a battery is not
connected to something of known potential, we have no idea what absolute potentials the terminals have.
We only know the difference between them is approximately the voltage stated on the package. Often we
hook one side of a power supply to the ground rod.
Figure-1.4 shows a battery grounded in two ways.
The left battery has its positive terminal grounded.
By definition its “positive” terminal is at zero
potential; it is not at positive potential. However
the positive terminal’s potential is still higher than
the negative terminal which is at true negative
potential.
The right battery of Figure-1.4 has its negative
terminal grounded. By definition its “negative
terminal is at zero potential; it is not negative.
However the negative terminal’s potential is still
lower than the positive terminal which is now at
true positive potential.
Figure 1.4 A single battery does not produce both
positive and negative potentials. If the positive
terminal is grounded the battery provides a negative
potential. If the negative terminal is grounded the
battery provides a positive potential. In either case
current flows the same direction.
It is quite common to find a power supply in a
laboratory that can be used with its positive terminal grounded, its negative terminal grounded, or neither
terminal grounded. The output connectors may even come with a ground strap that can be used or not used.
Michael D. Edmiston 1977, 2001
Chapter 1 — Page 8
Figure-1.5 shows how the output terminals might
look on this type of power supply. The circular
objects are “banana-jack” binding posts. Banana
plugs may be inserted into the center holes, or
wires can be tightened under the knurled nuts. The
ground terminal is connected to the building’s
ground rod through the power cord and the building
wiring. The rectangular object hanging from the Figure 1.5 Left: An ungrounded power supply
GND terminal in the left-hand picture is the (floating). Right: A negative power supply (positive
“ground strap.” When the ground strap is freely grounded).
hanging as in the left-hand picture, the power
supply is not grounded. There is a potential difference between the NEG and POS terminals that we can
measure with a voltmeter, but we do not know the absolute potentials of either terminal. This type of power
supply is called a “floating” power supply.
The right-hand picture of Figure-1.5 shows the ground strap connected to the positive terminal. This turns
the power supply into a negative power supply in the sense that it produces a potential that is definitely
negative with respect to ground. This is a versatile power supply because there are times we might
specifically want one of the three possible types of power supply (positive, negative, floating).
Unfortunately, seeing three terminals marked NEG, GND, and POS (or colored black, green, and red) is no
guarantee the power supply behaves like the one described in Figure-1.5. It’s possible the power supply is
actually a double power supply and has a true negative and a true positive at the same time.
Figure-1.6 shows how a double supply might work.
The “double power source” is depicted as two
batteries. The left battery has its negative terminal
grounded so it provides the positive potential to the
POS connector. The right battery has its positive
terminal grounded so it provides the negative
potential to the NEG terminal.
One hint to distinguish the power supply in Figure1.5 from that in Figure-1.6 is the presence/absence
of a ground strap. The power supply of Figure-1.6
cannot have a ground strap. Strapping GND and
Figure 1.6 A dual power supply providing true
POS together would “short-out” the left battery.
negative and true positive potentials has the
Strapping the GND and NEG together would
equivalent of two batteries inside.
“short-out” the right battery. “Short-out” means
the battery’s terminals are connect to each other
with no device in the circuit. Current flows from the (+) terminal directly to the (–) terminal. This runs
down the battery very quickly, and does no useful work. If the power supply is a transistorized supply (rather
than batteries) the short circuit could destroy it or at least blow a fuse.
The presence of a ground strap indicates a single supply such as Figure-1.5. The absence of a ground strap
might indicate a double supply, but not necessarily (perhaps the ground strap came off).
Michael D. Edmiston 1977, 2001
Chapter 1 — Page 9
1.1.10 Common versus Ground
In some instruments it is useful to define a reference point for the black voltmeter probe other than the
ground rod. When the circuit has such a reference point we refer to it as circuit reference or circuit common.
Some people refer to the circuit common as the circuit ground. This is confusing. If circuit common is not
connected to the ground rod it might be some potential other than zero. Calling something circuit ground
when it is not zero potential is at best awkward and at worst deadly. We will reserve the word ground for
those places which are truly at zero potential.
Some people call the ground rod the chassis ground since the metal chassis (the instrument case or frame)
is usually connected to the ground rod. We will simply call it ground, or better yet, earth ground.
When an instrument has a circuit common, it would be good if this were clearly marked on the circuit
diagram. Likewise, if it does not have a circuit common (i.e. the circuit reference point is truly ground) this
should also be clearly marked. One way to signify the difference would be to use different symbols for the
two possibilities. Circuit designers often attempt this but readers of the circuit diagram can easily be fooled.
There are three symbols for the two possibilities and there is no rigid
agreement as to what the symbols mean.
Figure-1.7A is not as popular but has the virtue of being fairly
unambiguous because it almost always means true earth ground.
Figure-1.7B usually means earth ground but is sometimes used for
ungrounded circuit common. Figure-1.7C usually designates circuit
common but does not guarantee isolation from earth ground. In this text
we will use Figure-1.7B for earth ground, and we will not use the other
symbols.
Figure 1.7 Symbols used to
indicate ground connections or
circuit commons. All three are
in current use.
1.1.11 Voltmeter Abbreviations
In the laboratory experiments throughout this text, the experimenter is often
told to measure a potential, potential difference, voltage, etc. Figure-1.8
shows how the meter is hooked to the device for the measurement
requested.
The top of Figure-1.8 shows what to do when a potential measurement is
requested. The text might say measure the potential at point A, or the text
might say measure VA, or the text might refer to an arrow in the drawing and
say measure the potential at the point in the circuit indicated by the arrow.
The bottom of Figure-1.8 shows what to do when a potential difference
measurement is requested. The text might say measure the potential
difference A relative to B, or the text might say measure )VAB, or the text
might refer to arrows in the drawing and say measure the potential
difference in the circuit as indicated by the arrows. Notice in this case the
arrows are joined and the black voltmeter probe is the arrow with the circle
on it. This indicates it is the zero or reference point for the potential
difference measurement.
Michael D. Edmiston 1977, 2001
∆
Figure 1.8 Definitions for
using a voltmeter to measure
a potential or a potential
difference.
Chapter 1 — Page 10
Lab 1.1 Potentials, Potential Differences, Grounding
Obtain two identical batteries. Any type and any voltage is okay but 9-volt
batteries with snap terminals are convenient. Alligator clips can be
attached to the terminals or two sets of snap leads can be obtained. The
examples will assume 9-volt batteries.
Find a connection to the ground rod. This might be the screw on an outlet
faceplate. It could be the metal case of an instrument. (The instrument
must be plugged in to a grounded outlet, but it need not be turned on.) A
water faucet works if you know you have metal plumbing.
In the figures below the arrows indicate places to measure true potentials.
Connected arrows indicate where to measure potential differences; the end
with the circle is the reference end (black probe). Use a digital voltmeter
because we want the meter to be capable of giving negative readings as
well as positive.
(A)
Use one battery. Connect the positive terminal to ground. Connect the
black voltmeter probe to ground. Measure the potential of each battery
terminal.
(B)
Use one battery. Connect the negative terminal to ground. Connect the
black voltmeter probe to ground. Measure the potential of each battery
terminal.
(Continue on Lab 1.1 next page...)
Michael D. Edmiston 1977, 2001
Chapter 1 — Page 11
(Continuation of Lab 1.1)
(C)
Use one battery. Connect the negative terminal to ground. Obtain two 10kohm resistors. Connect one resistor to the negative terminal; connect the
other resistor to the positive terminal; connect the two resistors together.
Measure the potential at each battery terminal and at the junction between
the resistors.
(D)
Repeat part (C) except unhook the negative terminal from ground and hook
the resistor junction to ground.
(E)
Connect the positive terminal of one battery to the negative terminal of the
other. Connect the free negative terminal to ground. Measure the potential
at each battery terminal. Measure the potential difference as shown
between the free positive terminal and the battery junction.
(F)
Leave the batteries connected. Unhook the negative terminal from ground
and hook the battery junction to ground. Measure the potential at each
terminal. Measure the potential difference as shown between the free
negative terminal and the free positive terminal.
(End of Lab 1.1)
Michael D. Edmiston 1977, 2001
Chapter 1 — Page 12
1.1.12 Discussion of Lab 1.1
Lab does little good if the experimenter blindly records data without thinking about the data. Sometimes the
thought occurs during the lab. Sometimes the thought takes place during a later analysis period. Usually it’s
a good idea to think both during lab time and during a later analysis time. The following analysis is an
example of what the student should think through. It would be good practice to keep a lab notebook or
journal in which the following types of observations are recorded..
Lab-Figure 1.1A demonstrates a battery with a grounded positive terminal does not really have a terminal
with a true positive potential. The total battery potential difference appears as a negative potential.
Lab-Figure 1.1B demonstrates a battery with a grounded negative terminal does not really have a terminal
with true negative potential. The total battery potential difference appears as a positive potential.
Lab-Figure 1.1C demonstrates it is easy to take a one-potential power source and get more than one potential
from it. The two resistors constitute a “voltage divider.” With two equal resistors the potential at the resistor
junction is the average of the terminal potentials. The divider in Lab-Figure 1.1C delivers the average of 0 V
and +9 V which is +4.5 volts. A divider with more resistors can give more potentials. Without additional
circuitry the potentials within the divider are not useful as “power supplies” because they can only deliver
small currents. We will discuss this problem later.
We just saw how voltage dividers give additional potentials. With the three defined potentials of a tworesistor divider it is not necessary that ground be hooked to the end. The center of the divider can be the
grounded connection. This allows simultaneous true positive and true negative potentials from one battery.
This trick is commonly done and we will later examine a power supply which works in this manner. In this
case it is important to realize the true positive and negative potentials are not the voltage marked on the
battery (or other power source.) Subtraction of the negative potential from the positive potential must yield
the battery voltage. Thus a 9-volt battery cannot simultaneously provide +9 V and !9 V. That would require
a total potential difference of 18 volts. Rather, a single 9-volt battery can provide any combination that
yields 9 volts total potential difference. (Actually, a 9-volt battery can yield about any voltage combination
you want, but voltages higher than 9 volts require a special circuit called a DC-to-DC converter.)
Lab-Figure 1.1E shows multiple batteries or other sources can be used to provide multiple voltages. Two
9-volt batteries can easily provide +9 V and +18 V. In this case note the negative terminal of the nongrounded battery is actually at a true potential of positive 9 volts. This lab also demonstrates the voltmeter
black probe can be removed from earth ground and placed at another point in the circuit. In this case it
allows one to measure the potential difference of the non-grounded battery. From the first measurements
we know the battery junction is at a true potential of +9 V and the free positive terminal is at a true potential
of +18 V. The potential difference between +18 V and +9 V, is +9 V minus +18 V, equals !9 volts. Thus
the meter should read !9 V.
Lab-Figure 1.1F again shows multiple sources can be used to provide true potentials of both polarities. When
one needs a power source that provides both positive and negative potentials the set-up in Lab-Figure 1.1F
is the simplest way to do it in theory. It may or may not be the economical or best way to do it in practice.
The last part of Lab-Figure 1.1F again shows how the black probe of the voltmeter can be placed somewhere
other than ground in order to measure a potential difference.
Michael D. Edmiston 1977, 2001
Chapter 1 — Page 13