We
usually try to start each lesson by giving reasons why you want to learn the
lesson topic. However, if you have ever had the misfortune of grabbing a
live wire with more than a few volts you might already have the answer to why
you want to learn about voltage. You've probably seen the signs that say
"Danger High Voltage", and you've probably talked about things or people being
"High Voltage". A high voltage individual is one with a lot of energy and
drive. That's apropos.
Still voltage is important - and not just to electrical engineers - because it
is the medium used to transmit information and energy in our world.
Goals
Here
are the objectives for this lesson.
Given an electrical circuit:
Be able to define voltages for elements within the circuit,
Be able to measure voltages for elements within the circuit.
What Is Voltage? - Ways Of Thinking About Voltage
Voltage
is a physical variable that can be thought of in different ways. Here are
a few ways you can think about voltage.
Voltage can be thought of as
the driving force (although it is not really a "force".) behind current.
Things like batteries are voltage sources. The voltage across the
terminals of a battery tends to stay pretty constant. When you connect a
device across the battery terminals a current flows through the device.
Current flows through
electrical elements when a voltage appears across the terminals of the element,
just like water flows through a pipe when a pressure difference appears across
the pipe. You can use that analogy to get started thinking about voltage.
More ways
of thinking about voltage are:
Voltage is an across variable
(Whereas current is a through variable, remember?). Water pressure that
causes water flow is also an across variable. We talk about pressure differences
and voltage differences.
Voltage is a concept that is
related to potential energy. Voltage is the electrical potential energy a
charge has by virtue of its position in space. Where the charge is affects
the energy it has because other charges exert forces on it. When forces
are exerted on the charge, then it may require energy to move the charge between
two points, or, conversely, the system may release energy as the charge moves
between two points.
Because
there are electrical forces there are concepts like potential energy that can be
used in electrical systems. What's more, the electrical forces obey an
inverse square law, just like gravitational forces, so a lot of concepts carry
over. Those gravitational force field concepts are important.
Electrical fields have much in common with gravitational fields, and a number of
those concepts carry over to electrical fields.
The
electrical force law and the gravitational are both inverse square laws.
Because the fundamental force law is the same, many of the concepts developed
for gravitational forces can be taken over to electrical concepts because the
underlying mathematics is the same. Those electrical concepts will be
almost exactly the same except that charge will play the role in electrical
forces that mass plays in gravitational forces. Here are some of the
important ideas that carry over.
Potential energy that is a
function only of position is a direct result of the inverse square force law.
Both gravitational masses and electrical charges obey an inverse square law.
Potential energy can be
converted into other forms of energy. In a gravitational field, masses can
fall together (due to mutual attraction) and the potential energy can be
converted to heat and kinetic energy.
A mass can acquire kinetic
energy in an gravitational field and later that kinetic energy could be
converted to heat. Charges attached to masses can acquire energy in an
eletrical field, and that kinetic energy can be converted to heat.
The many
concepts that carry over from gravitational systems help to make voltage a much
richer concept. Think of some of the implications.
If you pull two masses apart
(by lifting a weight to a higher position on the earth, for example) you put
potential energy into the system. If you pull two attracting charges apart
you put potential energy into the system.
That potential energy can be
converted into other forms of energy. If you have a charge with potential
energy, you can generate light, heat, mechanical motion and you can even store
chemical energy.
Voltage Concepts
In
electrical fields, we will want to think in terms of the potential energy per
unit of charge. Near the earth's surface the potential energy of a mass,
m, h meters above the surface is mgh. The potential energy per unit mass
is just gh. Voltage is the potential energy per unit
charge for a charge in an electrical force field.
There are consequences of the inverse square law for electrical forces.
Generally, those consequences are similar to what happens in gravitational
systems.
In an electrical field, or in
any conservative field like a gravitational field, we will have to do the same
amount of work to move the charge between any two points A and B, no matter what
path we take in moving the charge. Work done in a conservative field is said to
be "path independent".
The potential energy in a
gravitational field and the voltage in an electrical field (potential energy per
unit of charge) are functions of position only.
One
important consequence is a relationship between energy put into a charge as it
moves.
If we move a charge from point
A to point B, and put a given number of joules of work into the charge, we will
recover exactly the same number of joules from the charge if it moves back from
point B to point A. If we move the charge through any closed path or
circuit, there will be no net energy input to the system and no net energy
recovered from the charge.
If we move a charge from point
A to point B, the number of joules of work we put into the charge can be
calculated by multiplying the charge, Q, by the voltage difference between
points A and B, Vab.
Problem
P1
What are the units of voltage in the MKS system? Remember, that voltage
is potential energy per
unit of charge.
We can draw a number of analogies between voltage and gravitational potential
energy. Consider the circuit below. The element shown in yellow
"pumps" charge from a lower potential - the bottom terminal of the yellow
element, to a higher voltage (potential energy per unit charge, remember?) at
the top of the yellow element. That's like lifting a weight from a low
position (a position with lower potential energy) to a higher position (one with
more potential energy). Click to button to see what happens as the charge
moves around the circuit.
Problem
P2
The yellow element in the simulation above adds energy to the charge. What
kind of element could do that?
There's a point to the simulation above. A battery, or any other voltage
source, is a sort of charge pump. If you buy a battery and you connect
something to it, it will supply charge at some specified voltage to your applied
electrical load. If the charge is pumped up to nine (9) or twelve (12)
volts, for example, then when you connect a load to your battery charge will
flow out of your battery, through the load. Energy will be transferred to
your applied load from the battery.
What
happens in this situation with regard to the energy involved? When the
charge goes through the battery, and is "pumped" up to, say, twelve (12) volts
it acquires potential energy. As it flows through the load it gives up
this potential energy to the load. If the load is a motor that energy
might be transformed into mechanical energy, potential (by lifting a weight) or
kinetic (by turning a flywheel). If the load is a light bulb, the energy
is transformed into light and heat.
Here's a simple circuit. A battery (remember the special symbol for a
battery) is connected to two elements in series. Charge/current flows out
of the battery, through element "1", out of element "1", into element "2" and
out of element "2" back into the battery. As the charge flows through the
battery it acquires energy. Some of that energy is given up to element 1,
then some of that energy is given up to element 2. Note that:
Energy Gained in the battery = Energy lost in Element
"1" + Energy lost in Element "2".
Note
that this is simply a statement of Conservation of Energy.
Now, if we know the voltages at points in the circuit, we can compute the work
done as the charge moves (current flows) around the circuit. Let's imagine that
we have two (2) couloumbs of charge and we move it around the circuit shown
above. Let's compute how much work will be done as the charge moves
through the circuit. We will pose that as a sequence of short problems.
Problems
P3
Here's the first question for you. In the circuit above, the battery is a
twelve volt battery. You move 2 coulombs of charge from the bottom of the
battery to the top of the battery. Click on the button you think gives the
value of the work that is done moving the charge.
P5
Now, consider what happens when the charge flows through Element #2.
First, determine whether the charge gains energy or loses energy as it flows
through Element #2.
Given an electrical circuit:
