Voltage
Why Do You Need To Know About Voltage?
Voltage
Measuring Voltage
Problems
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Voltage

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.

P4   After the current goes through the battery, it then flows through Element #1.  Element #1 has 9 volts across it.  How much energy is transferred to Element #1 as the charge flows through it?  (Alternatively, how much work does the charge do?)  Give your answer in Joules.

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.

P6   How much energy does it lose going through Element #2.  Give your answer in Joules.

P7   Now, let's test how well you really understand all this stuff.  What's the voltage across Element #2?  Give your anser in volts.

What points should you remember from this?  If you can put potential energy into a charge (as in a battery, for example) then whatever energy the charge acquires in the process is transferred totally to whatever elements the charge passes through as it wends its way back to the point where it has no potential energy.

Electrical engineers would say this slightly differently.  Here's how they would say it.

• If a charge is raised from zero voltage (zero potential energy) to a higher voltage (as in a battery, for example), then when that charge moves back to the point of zero potential energy it passes through voltages that sum to whatever the voltage was that it passed through to acquire the energy.
This is really a statement of conservation of energy, and you can realize that once you remember that voltage is really potential energy per unit of charge.

We also need to be more precise in our discussion of voltage.  Engineers communicate with symbols, and they use special symbols to show voltages.  Let's look at the circuit we used earlier.

We have added symbols to define all of the voltages in the circuit.  For example, we have defined a symbol, VB, that represents the voltage across the battery.  For the voltage, VB , as we have defined it, we can compute the energy added to a charge, Q, when it moves from the bottom of the battery (at the "-" sign) to the top of the battery (at the "+" sign) as Q*VB.  Let's get a complete set of statements about what happens as charge moves around this circuit.

• As a charge, Q, moves from the bottom of the battery (at the "-" sign) to the top of the battery (at the "+" sign), the charge gains an amount of energy, Q*VB.  The units are coulombs for charge, volts for voltage and joules for energy.
• As a charge, Q, moves from the top of element #1 (at the "+" sign) to the bottom of element #1 (at the "-" sign), the charge loses an amount of energy, Q*V1.
• As a charge, Q, moves from the top of element #2 (at the "+" sign) to the bottom of element #2 (at the "-" sign), the charge loses an amount of energy, Q*V2.
We can generalize these statements.
• If we have used the convention introduced above - with "+" and "-" signs - for voltage, then when a charge, Q, moves from the end of the element labelled with a "-" sign to the end of the element labelled with a "+" sign, the charge gains QV joules, where V is the voltage across the element.
Now, it's time for you to answer a few questions.

Questions

Here is a more complex circuit.

Imagine that you have a charge, Q, which is moved between various points in the circuit.  The points we will consider are marked with little green squares, and have alphabetical labels (A through F).  Answer the following Questions.

Q1.  If a charge moves from point B to point C, how much energy does the charge lose?  Be careful with your signs.

Q2.  If a charge moves from point C to point D, how much energy does the charge lose?  Be careful with your signs.

Q3.  If a charge moves from point D to point E, how much energy does the charge lose?  Be careful with your signs.

We'll repeat the diagram so you don't have to scroll to answer the last few questions.

Q4.  If a charge moves from point E to point F, how much energy does the charge lose?  Be careful with your signs.

Q5.  If a charge moves from point F to point A, how much energy does the charge lose?  Be careful with your signs.

Problem

P8   Assume that you have a twelve volt battery.  How many joules of work would you have to do to move 0.4 couloumbs  from the negative terminal to the positive terminal?

Finally, you may have noticed a funny little symbol connected to point E in the drawing in the questions.  That symbol is a ground symbol, and it has some importance.  Ground is the reference voltage from which all other voltages in a circuit can be measured.

Let us consider a battery connected in a piece of electronic equipment.  Very often there is some obvious reference from which you can measure voltage.  In homes and buildings that reference is the ground. Interestingly, ground level is often used as a reference when you compute potential energy of a weight that has been raised, so that's another little thing that electrical and mechanical systems share.

The "electrical community" has come to agreement that the potential of the earth itself is the reference from which voltages are to be measured.  In many pieces of electrical and electronic instrumentation there is a terminal connected directly to ground.  Those terminals look like the following.  The black connector on an electronic instrument will be the ground connection.  (And, the British will refer to it as the "earth" connection.)

Like mechanical potential energy, electrical potential energy and voltage are measured from a reference.  For mechanical energy, that might be ground level.  It's just that some reference needs to be chosen.  (And, it is chosen, not pre-ordained by nature!)

Electrical systems need a reference and the reference usually chosen is ground.  That means the reference is the earth itself.  (In America, we usually refer to that as "ground" while the English refer to it as "earth".) In any event, in any piece of electrical or electronic equipment, "ground" voltage is always available.  It's the voltage at the third prong of the plug you put into the wall socket.

In any event, the voltage level of the ground in your vicinity is chosen as a reference voltage, and often voltages are measured from that reference.  Since we must always talk about voltage differences, we should realize that if we say that some electrical terminal (a point in space) is at a voltage level of 120 volts, we mean that the voltage difference between that point and ground is 120 volts.

• Rule to Remember:  Whenever you talk about a voltage, you are always talking about a voltage difference! - and you should specify the two points in space where that difference exists.
Shown below is a picture of a wall plug.  The small circular hole at the bottom is connected directly to ground.  If you trace out the wiring in your home, you should find that the wire that makes the connection to the circular hole is connected (behind the walls) to a water pipe, or something else that makes good contact with the ground on which the house is built.

What's more, if you measure the voltage between the other connections and ground you will usually find that one of them is at a voltage of 120 volts.  We would say that that voltage is 120 volts measured with respect to ground.  We take advantage of that connection in electronic instrumentation and many instruments can measure voltage with respect to ground, or can generate a voltage relative to ground.  This is a source of voltage that is very common.

Finally, the last important concept.  Don't try to plug a plug into the picture above.  Use a real wall plug.

At this point, you've started to get acquainted with voltage.  If you have to use circuits with live voltage you'll need to know how to measure voltage, and a few other things.  That's the next section.

Measuring Voltage

If you deal with circuits you will need to be able to measure voltages in circuits.  That's the one skill you absolutely must have if you want to check that a circuit is operating properly.  You know that Murphy's law prevails.  If anything can go wrong, it will.

You will always need to check a circuit's operation to see if it is working correctly.  Actually, you'll probably need to check it to find out why it isn't working.  Many times you will do that using a voltmeter.  In this section we'll discuss how to use a voltmeter to measure voltages in an operating circuit.  (Click here for a longer discussion of measuring voltage, and links to some experiments.)

There are many other situations in which you would want to be able to measure voltage.  For example, you might have an LM35 temperature sensor.  Then the output of the sensor is a voltage that is proportional to the temperature of the sensor.

We will give you a choice here.  You can continue in this lesson, or you can read the lesson devoted entirely to voltage measurements.  Click here to go to that lesson which covers numerous laboratory measurements and gives you several experiments to perform.

Using a Voltmeter

Here's a representation of a voltmeter.  For our introduction to the voltmeter, we need to be aware of three items on the voltmeter.

• The display.  This is where the result of the measurement is displayed.  Your meter might be either analog or digital.  If it's analog you need to read a reading off a scale.  If it's digital, it will usually have an LED or LCD display panel where you can see what the voltage measurement is.
• The positive input terminal, and it's almost always red.
• The negative input terminal, and it's almost always black.
Next, you need to be aware of what the voltmeter measures.  Here it is in a nutshell.
• A voltmeter measures the voltage difference between the positive input terminal of the voltmeter and the negative input terminal.
That's it.  That's what it measures.  Nothing more, nothing less - just that voltage difference.  That means you can measure voltage differences in a circuit by connecting the positive input terminal and the negative input terminal to locations in a circuit.
Next, we'll look at a circuit diagram.  We'll show a voltmeter connected to the circuit diagram - a mixed metaphor approach.  Forgive us for that, but let's look at it.  It's right below.

Here's a voltmeter shown connected to a circuit.  This shows where you would place the leads if you wanted to measure the voltage across element #4.

• Notice that the voltmeter measures the voltage across element #4, +V4.
• Notice the polarity definitions for V4, and notice how the red terminal is connected to the "+" end of element #4.  If you reversed the leads, you would be measuring -V4.
Here's a portion of a circuit board.  You want to measure the voltage across R27.  Click on where you should put the voltmeter leads.

What If ?

At this point, you're starting to become comfortable with voltage.  Don't become too comfortable.  Always respect two things about voltage.

• It can give you a shock, and a large enough voltage can be lethal.
• It's more complicated than we've really indicated so far.
You Need To Know More About Voltage

So far, we've just examined voltage as though it were across one device.  However, if we look at the example circuit we used before we realize that there are lots of voltages in this circuit.  If we measure them, how do we know our measurements make sense?  There are laws that voltage obeys.  The most important one is Kirchhoff's Voltage Law (click here to go to the lesson!), (KVL) and it's the subject of another lesson.  It is an important relationship that voltage obeys, and it is the starting point for analysis of circuits of any complexity. That's it for this lesson.  You can exit this lesson and start another lesson by clicking the up-pointing arrow below.  Or you can go directly to several places from this page.  You can use any of these hotwordsto take you to a lesson of your choice.

Problems