Voltage

1
Voltage
Potential Energy
A bucket containing 1kg of water
Its potential energy is mgh weight x
height Its potential energy per kg is g x h
joules / kg.
h
Ground Level
2
Voltage
Potential Energy
Suppose at ground level theres a water wheel
which drives a generator. We pour out the
bucket, the water strikes the water wheel, and
its kinetic energy is completely converted to
electricity. The water now has no kinetic
energy, and since it is at ground, zero potential
energy. Each bucket generates 1 joule of energy,
or 1 joule per kg.
h
Ground Level
In England, this is called earth.
3
Voltage
Potential Energy
Now suppose we raise the height from which the
water is poured to 2h, so the waters potential
is 2gh joules/kg. We also raise the water wheel
to a height h above ground. Now, the water has
potential gh joules/kg. after turning the wheel,
because it is still h meters above ground. If we
call the initial potential p1, and the potential
after turning the wheel p2, the enegry converted
to electrical energy is (p1 p2) joules/kg.
p1
h
p2
h
Ground Level
4
Voltage
Potential Energy
Suppose we replace the water in the bucket with a
quantity of electrical charge, and we place a
quantity Q of charge at ground level. Now,
instead of gravity attracting water, we have
charge attracting charge. Lets say each bucket
now contains 1 Coulomb of charge, opposite in
sign to Q (so the electrostatic force is
attractive). The water wheel is replaced by a
perfect motor, which converts electrical energy
to mechanical energy.
p1
h
p2
h
Ground Level
Q
5
Voltage
Potential Energy
Potential p1 is now expressed in joules per
Coulomb, as is p2. The energy converted to
motion is now equal to (p1 p2) joules per
Coulomb, or (p1 p2) Volts. Lets replace the
symbol p (for potential) with v (for voltage).
Voltage is a measure of electrical potential.
p1
h
p2
h
Ground Level
Q
6
Voltage
Potential Energy
In our original, water-based example, we could as
easily pour buckets of water into a pipe, which
feeds the turbine (water wheel). If we pour 1
bucket of water per minute, the flow rate is 1 kg
/ min, or its equivalent in gpm.
h
Ground Level
7
Voltage
Potential Energy
Instead of pouring buckets of water, we could
have a pump which produces a flow rate of 1
kg./min (or its equivalent in gpm. After
turning the turbine, the water drains into a
reservoir.
Pump 1 kg/min.
8
Voltage
Potential Energy
The pump takes water from the reservoir, and
makes the pressure in the feedpipe whatever it
must be to produce a flow of 1kg/min. Water
continuosly circulates from the reservoir,
through the pump, through the turbine, and back
to the reservoir. The amount of water in the
system never changes. This is a closed circuit
Pump 1 kg/min.
9
Voltage
Potential Energy
Now lets consider an analogous electrical
circuit.
The battery takes charge from ground
(reference, or zero, potential) and forces it to
flow through the wire (think of it as a charge
pipe) to the motor. After its energy has been
converted, the charge returns to ground.

Motor
Battery
-
Ground
10
Voltage
Potential Energy
A pump produces water under pressure, which
forces it to flow in the pipe over the resistance
of friction, and the resistance of the generator
which the turbine drives.

The battery forces charge to flow through the
wire, against the resistance of the wire (it
isnt a perfect conductor), and against the load
of the motor. This force is called electromotive
force, or EMF. Sometimes its called potential.
Its measured in volts , and also called Voltage.
Motor
Battery
-
Ground
11
Voltage
Potential Energy
To measure Voltage, use a Voltmeter.
Wed like to measure the amount by which voltage
decreases as current flows through R1, from V1 to
V2. This will tell us how much energy per
Coulomb is converted to heat by the
resistor. First, measure the voltage (referenced
to ground) at V1.
V1

R1
-
Battery
V2
R2
Ground
12
Voltage
Potential Energy
To measure Voltage, use a Voltmeter.
Next, measure the voltage (referenced to ground)
at V2. Subtract V2 from V1.
V1

R1
-
Battery
V2
R2
Ground
13
Voltage
Potential Energy
To measure Voltage, use a Voltmeter.
Heres a simpler way Connect the reference
(ground) lead to V2, and the measurement lead to
V1. The meter now reads the voltage drop across
R1.
V1

R1
-
Battery
V2
R2
Ground
14
Voltage
Potential Energy
To measure Voltage, use a Voltmeter.
Note Ideally, no current flows through the
Voltmeter. It has infinite resistance.
V1

R1
-
Battery
V2
R2
Ground
15
Current
To measure current, use a Currentmeter Ammeter.
I
The Ammeter must be inserted in the circuit in
such a way that the current we want to measure
flows through the meter. The Ammeter does not
change the voltage in the circuit, since there is
zero voltage drop across the meter. It looks
like a short circuit.

Battery
-
Motor
16
Current
To measure current, use a Currentmeter Ammeter.
What happens if we accidentally connect the
Ammeter as if it were a Voltmeter? Weve just
shorted out the motor. A very high current,
which is not the current we wanted to measure,
tries to flow through the meter and probably
blows a fuse or causes other damage.

Battery
-
Motor
17
Current
To measure current, use a Currentmeter Ammeter.
What happens if we accidentally connect the
Ammeter as if it were a Voltmeter? This is a
common mistake for beginners in the lab. Dont
do it!!!

Battery
-
Motor
18
DC Voltage
There are two types of voltage (and current)
AC, or alternating current, and DC, or direct
current. The voltage available at a wall socket
is 120 Volts AC. This type of voltage is the
origin of the term AC, because it alternates
between positive and negative. If we were to
plot this voltage versus time, we would see that
it has a particular shape called a sine wave, or
sinusoid, and that its positive exactly half the
time, and negative half the time.
Positive Voltage
t
Negative Voltage
19
DC Voltage
Direct Current, DC, is called direct because it
does not alternate. It remains always positive
or always negative. Strictly speaking, a DC
voltage (or current) doesnt vary at all its
always the same. This is an idealization,
because every source of voltage is turned on or
off at some point in time, and may vary by a
small amount over a long period of time.
Positive Voltage
t
Negative Voltage
20
DC Voltage
What about a voltage which varys with respect to
time, but is always either positive or
negative? In a less strict sense, this is DC
because it does not alternate. However, you will
see in the next course that any such time-varying
DC voltage (or current) may be expressed as the
sum of a true DC voltage and one or more sine
waves a DC part, or component, and an AC
component
Positive Voltage
t
Negative Voltage
21
DC Voltage
The pulse trains which carry digital information
within computers or across computer networks can
be expressed as a DC component and an AC
component. The AC component is a sum of many
sinusoids, called a Fourier series or Fourier
transform. This is why CPET majors and EETs
taking the computer networking option are forced,
often kicking and screaming, to take the DC and
AC circuits courses.
Positive Voltage
Digital Pulse Train
t
Negative Voltage
22
Ground and Common
Remember our example of potential energy, using
buckets of water from a height h or 2h? The
potential energy with respect to the ground, in
this figure, is mg(2h). The energy with respect
to the turbine is mgh. We need to define
potential (either electrical or mechanical) with
respect to a reference level. In this example,
ground was a convenient reference. In
electrical circuits, the reference may be
arbitrary, but it is called ground or common.
p1
h
p2
h
Ground Level
Q
23
Ground and Common
Consider a pair of batteries connected end-to-end
(in series) as they would be in a flashlight. If
you examine a flashlight, youll see that the
negative terminal of the bottom battery is
connected to the metal case of the flashlight.
Current flows out the upper positive terminal,
through the bulb, and returns to the bottom
negative terminal through the case. This is an
example of chassis return the case, or chassis,
is used as the common or ground point in the
circuit. The ground point of the circuit is the
point we define as having a voltage of 0 Volts.
Voltages at other points in the circuit are
measured with respect to ground (unless noted
otherwise). Therfore, in this circuit, the upper
terminal has a potential of 3 Volts.
3 V

-
1.5 V

1.5 V
-
0 V
Chassis Return Symbol
24
Ground and Common
It would be no less correct to call the point
where the positive terminal of the lower battery
touches the negative terminal of the upper cell
(The two cells together really comprise a
two-cell battery) as common or ground. In this
case, the lower negative terminal is at a
potential of -1.5 V with respect to common, and
the upper positive terminal is at 1.5 V. We
havent changed the flashlight, just the point we
call ground, or 0 V. The voltage across the two
cells is 1.5V (-1.5V), or 3V unchanged. The
ground symbol used here is the analog common
symbol.
1.5 V

1.5 V
-
0 V

1.5 V
-
-1.5 V
Chassis Return Symbol
25
Ground and Common
If we connected the case of the flashlight to the
earth, via a cable to a copper rod driven into
the dirt, it would be appropriate to use the
earth ground symbol. In practice, all three
ground or common symbols are used somewhat
interchangeably.
3 V

-
1.5 V

1.5 V
-
0 V
Earth Ground Symbol
26
Batteries
Batteries store energy in chemical form, which is
converted to electrical energy by a chemical
reaction as energy is drawn from the batter. A
battery has a positive terminal or a negative
terminal, and produces a potential difference (a
voltage) between the two terminals. Flashlight
batteries (AA, A, C and D) are single cells, with
a cell voltage (for alkaline cells) of 1.5 V.
Some batteries, like 9 Volt batteries, contain
more than one cell. The cell voltage is still
(for alkaline batteries) 1.5 V, so a 9-Volt
battery contains 6 cells in series.
3 V

-
1.5 V

1.5 V
-
0 V
Earth Ground Symbol
27
Batteries
There are many different battery chemistries
lead-acid (car batteries), carbon-zinc (the
cheapest), alkaline, nickel-cadmium, and
nickel-metal-hydride (Nimh), to name a few.
These chemistries may have different cell
voltages. Nickel-cadmium (Ni-cad) cells are
nominally 1.2 Volts, Nimh cells are also 1.2 V.
3 V

-
1.5 V

1.5 V
-
0 V
Earth Ground Symbol
28
Batteries
The amount of energy which can be drawn from a
cell depends on its physical size and its
chemistry. A D cell stores more energy than a AA
cell, if both have the same chemistry. The
energy capacity also depends on the chemistry
Alkaline cells store more energy than Ni-cad
cells of the same size.
3 V

-
1.5 V

1.5 V
-
0 V
Earth Ground Symbol
29
Batteries
The energy capacity of a battery is specified in
Amp-hours, or milliampere-hours. A AA cell with
a capacity of 1500 mA-H. Can have a current of
100 mA. Drawn from it for 15 hours, or 150 mA.
For 10 hours, etc., before its voltage drops
below the minimum specified voltage.
3 V

-
1.5 V

1.5 V
-
0 V
Earth Ground Symbol
30
Electronic Power Supplies
Positive Supply
An electronic supply typically takes 120 V AC and
converts it to a fixed or adjustable DC voltage
of a greater or lesser magnitude. It has two
terminals, V and V-. If the negative terminal,
V-, is connected to the common point of the
circuit, its a positive supply because the
terminal which is not connected to the common
(zero voltage) point is positive. If the V
terminal is connected to common, and therefore
has a voltage of zero, its a negative supply
V
V-
Negative Supply
V
V-
31
Electronic Power Supplies
Positive Supply
0 20 V
0 20 V
5 V
Earth Common
V-
V
V-
V-
V
V
5V
-15V
15V
Its not uncommon to find one box containing two
or more power supplies. Heres a common example
Two 0 to 20 Volt adjustable supplies, along with
a fixed 5-Volt supply. We may use one of the
adustable supplies as a negative supply and the
other as a positive supply to provide 15 V and
-15 V for analog circuitry, and the 5-Volt supply
for digital circuitry, as shown here.
32
Bubble Notation
We may simplify a schematic by using a sort of
shorthand. We can leave out the symbol for a
battery or power supply, and simply show a bubble
with the supply voltage next to it. It is
assumed that the bubble is connected to a voltage
source (such as a battery) and that anything
shown as connected to the bubble is at that
voltage. Of course, anything connected to the
ground symbol has a voltage of 0 V.
9 V
9 V

9 V
-
0 V
33
Node Voltage
Node is a very important term in the study of
electrical circuits. A node is a point where two
or more circuit elements are connected together.
In the circuit below, the battery and the motor
are elements. The ground symbol is not an
element.
Node A
Each terminal of a circuit element must be
connected to a node, nearly always each to a
different node. This circuit has two nodes,
shown by the dotted lines.

Motor
Battery
-
Node B
Ground
34
Voltage
In this circuit, the voltmeter is also a circuit
element. The circuit has 3 nodes.
Node a
Each node has a node voltage its potential with
respect to ground. The voltage at node a is 9V,
and node cs voltage is 0V. Node bs voltage
might be 5V. We can write

9V
R1
-
Battery
Node b
R2
Node c