Do-It-Yourself Probeware

A Guide to Experiments With Inexpensive Electronics

Draft May 25, 2007

Robert Tinker
and the ITSI Team
The Concord Consortium
Copyright 2007

Table of Contents

Table of Contents..................................................................................................................... 2

Introduction............................................................................................................................... 4

Why Probeware?.................................................................................................................. 4

Why Do It Yourself Probeware?........................................................................................ 4

About This Guide.................................................................................................................. 5

Summary of the Sections..................................................................................................... 6

Credits.................................................................................................................................... 7

Section 1: Safety........................................................................................................................ 8

Section 2: Basics....................................................................................................................... 10

Charge.................................................................................................................................. 10

Current................................................................................................................................. 11

Voltage................................................................................................................................. 11

Resistance............................................................................................................................. 12

Capacitance.......................................................................................................................... 13

Inductance............................................................................................................................ 14

Equivalent Resistance......................................................................................................... 14

Matching Outputs and Inputs........................................................................................... 15

Section 3: The Kit Parts.......................................................................................................... 16

The Parts in the Kit............................................................................................................. 16

Mug Shots............................................................................................................................ 18

Section 4: Using the DMM..................................................................................................... 21

Plug it in and Turn it On.................................................................................................... 21

Measuring Voltage............................................................................................................. 22

Measure Resistance............................................................................................................ 22

Test the Clip Leads............................................................................................................. 23

Trouble Shooting the DMM.............................................................................................. 23

Don’t Measure Current..................................................................................................... 23

Section 5: A First Probe.......................................................................................................... 24

The Parts You Need........................................................................................................... 24

Overview............................................................................................................................. 24

The GoLink.......................................................................................................................... 24

The TMP36 Sensor.............................................................................................................. 26

The Experiment Board...................................................................................................... 27

The Complete Circuit......................................................................................................... 27

Creating a Probe................................................................................................................. 29

Section 6: Three-Wire Probes................................................................................................ 31

Magnetic Field..................................................................................................................... 31

Rotation................................................................................................................................ 32

Other Three-Wire Sensors................................................................................................. 34

The TDK relative humidity sensor................................................................................... 34

Section 7: Experiments with Three-Wire Probes............................................................... 35

Temperature........................................................................................................................ 35

Map the Magnetic Field..................................................................................................... 35

A Pendulum......................................................................................................................... 35

Section 7: Half-Bridge Circuits.............................................................................................. 36

What is a Half-Bridge?....................................................................................................... 36

Measuring Light with the Phototransistor..................................................................... 36

Measuring Force with Conductive Foam....................................................................... 37

Measuring Galvanic Skin Response................................................................................. 38

Section 8: Amplifier Circuits.................................................................................................. 41

Voltage Amplifiers............................................................................................................. 41

Example: Thermocouple.................................................................................................... 42

Example: Small Magnetic Fields....................................................................................... 46

Current-to-Voltage Amplifiers......................................................................................... 46

Example: LED as Detector................................................................................................. 47

Section 9: Calibration............................................................................................................. 48

Overview............................................................................................................................. 48

Linear Probes...................................................................................................................... 48

Non-Linear.......................................................................................................................... 48

Section 10: Noise Reduction.................................................................................................. 49

What is Noise?.................................................................................................................... 49

Keeping Noise Out............................................................................................................. 49

The RC Filter....................................................................................................................... 49

Example: The Motion Detector......................................................................................... 50

Introduction

This guide is designed for teachers who want to offer students the ability to undertake exciting, meaningful science experiments while also learning a bit of very useful electronics. It was developed for the Information Technologies for Science Investigations (ITSI) project at the Concord Consortium.

Why Probeware?

The ITSI project gives you access to the best and latest technology-enhanced materials for secondary science. The materials are classroom-tested, and research-based activities. They balance the use of real experiments using probes and virtual ones using computational models. This guide supports the “real” experiments used in the ITSI project.

It is important that every student have frequent lab experiences. Labs give students unique opportunities to focus on critical concepts and to understand how these concepts play out in real contexts. One of the most important goals of labs is to impart experimental skills that enable students to become increasingly independent so they can learn thing on their own.

One of the most valuable uses of computers in science education is as instruments that can sense, record, and display data in real-time. We invented the term “Microcomputer Based Labs” or MBL to refer to this kind of application, back when microcomputers were rare and amazing devices. Now that they are ubiquitous, the term seems antiquated and we have shifted to using “probeware” instead.

Probeware is educationally important for many reasons. Its use of computers accurately reflects how most modern science is done. Compared to hand data collection, it is faster, allowing students to undertake more experiments at a faster rate. Most importantly, it provides fast feedback and it helps build strong associations between phenomena and their abstract representation. A student who warms a temperature sensor with her finger and sees the graph of temperature against time immediately understands the graph. Any student using a motion detector who sees time graphs of velocity and distance, immediately understands how these are related.

Why Do It Yourself Probeware?

The ITSI Do-It-Yourself Probe Kit provides the electronics and tools you need to build and test circuits that can measure a wide range of properties and get these into to computer.

Probes can be expensive. A comprehensive collection for one lab station starts at $1,000 or more. If your school can afford this, by all means buy them from one of the wonderful, dedicated companies that supply probeware.[1] As we were planning the ITSI project, we wanted to supply every participant with a classroom set of probeware, but that was completely impossible. Instead, we chose to assemble an inexpensive probe kit that includes all the parts needed for 14 different probes that can be used in scores of experiments.

We advocate working kit construction into the labs associated with science courses. There are two advantages to this, in addition to the cost savings: students will learn some valuable electronics and they improve their experimental skills.

The kit gives a taste of electronics, physics, and computer interfacing. The electronics is not hard and provides a nice introduction to the hardware side of information technology. This is important for students, because few in IT have even the slightest understanding of electronics, and those that do are uniquely prepared for a range of rewarding positions. The electronics that is used is also a great introduction to electrical engineering and applied science. Every sensor is based on some basic scientific principle at the atomic level and these same principles are at the heart of many chemical and biological phenomena.

The national standards and many of the state standards call for extended student investigations. Students often come up with wonderful ideas for investigations that cannot be done for lack of instrumentation. The project may require data acquired very quickly or slowly over weeks; the effect might be difficult to measure, such as the body temperature of a cockroach or the force exerted by a gecko foot; or the experiment might require measuring a quantity such as pressure that does not match available equipment and budgets. Students who are able to create their own instruments using the ideas in this guide, can undertake a much larger range of original investigations.

About This Guide

Even though this guide requires only a limited number of electronics parts, it provides a solid introduction to electronics, sensors, and some important experiments that can be done with them.

Do not be overwhelmed by all the information we have included. This guide is a reference, not a text. Feel free to skip around and use just the parts you need at any one time. We wanted to make it a reference that teachers and students can return to over and over.

This guide is developed for teachers. Students would not be expected to work through the guide. Instead, you should decide what probe-based experiments you want to offer and then work backward to determine exactly how much of the content of this guide is needed for your students. ITSI workshop participants are welcomed to excerpt from this guide to create appropriate student materials. We fully support this use of the guide, as long as you give us credit and don’t sell your excerpt. We encourage you to post your student materials on the ITSI website so other teachers can use them as well.

We have purposely minimized the parts that this guide needs to keep the price of the components down. By searching the Internet for leftovers and ordering 650 items at once, we were able to keep the total cost of each kit to $25, exclusive of the two Vernier parts. Some of these parts are a bit sub-standard, but even these provide an opportunity for learning. Students should never trust their equipment and should develop a skeptic’s approach that includes always double-checking everything.

Summary of the Sections

This guide starts with some important safety information in Section 1. Although the approach we have developed minimizes hazards, every teacher and student should be aware of potential dangers and get in the habit of being careful.

The bulk of the guide should be seen as a series of notes and applications that can be approached in any order, depending on the knowledge of the reader. For students with no understanding of electricity, Section 2: “Basics” is designed to help sort out current, voltage, resistance, and some basic concepts that will be used over and over. Even someone familiar with these terms will find useful information in the “Matching Outputs and Inputs” part.

Section three lists the parts in the ITSI kit with pictures. The ITSI kit includes a very useful digital multimeter (DMM). The fourth section discusses how to use this meter and how to fix it if something goes wrong.

In Section five, you make your first probe, a temperature sensor that can be used in many different experiments. This requires the minimum of electronics—simply connecting three wires from the sensor to the computer interface. The hardest part of this project is figuring out how to put the sensor on a wand of some sort to make a probe that can be used conveniently.

Actually, there are a number of sensors like the temperature sensor that require connecting only three wires. This type of sensor is addressed in the following two sections. The magnetic field probe and the “rotation sensor” are examples that are included in the ITSI kit. Pressure, humidity, and acceleration sensors are also described that are not in the kit because of cost, but are covered because they might be useful in student projects. The electronics for the three-wire sensors are covered in Section five and experiments that use them are in Section six.

In Section seven, we cover the simplest possible circuit that requires more than direct connections between the sensor and interface. This is the so-called “half bridge” circuit that needs just a resistor in addition to the sensor. The light detector and conductive foam force sensor use this circuit as well as the skin conductivity experiment.

There are many situations in which the electrical signals are too small for the interface to detect. This happens for some sensors or when greater sensitivity is needed. For instance, the ITSI kit includes thermocouple wire that can be used to sense small temperature differences, but only generates a twentieth of a millivolt for each degree difference. A voltage amplifier is needed to multiply this signal by 1,000 before the interface can detect it. Section eight shows how a simple but powerful amplifier can be built for the thermocouple and magnetic field sensor. It also contains a circuit for amplifying small currents, such as those generated by a LED when used to detect current.

Data from probes enters the computer as raw data represented as binary numbers from zero to 4,095. These numbers are related to the temperature, magnetic field, or other physical quantity detected by the sensor. The process that establishes the exact mathematical relationship between the physical quantity and the raw data is called calibration and is covered in Section 9.

Electrical noise originates as unwanted signals that get mixed into the signal generated by a sensor. Some sensors, like the motor used in Second 11 are inherently noisy. Noise also often limits how much amplification is possible, because the amplifier not only amplifies noise, but can contribute noise as well. Even a resistor generates noise due to the random thermal motion of its parts. Section 10 shows how to reduce noise by keeping it out in the first place and filtering it once it gets in.

Section 11 describes some clever sensor tricks that use some common devices that are not normally considered as sensors. The section shows how DC motor can measure distance, a magnetic field sensor can measure force, and a thermocouple can measure humidity.

Every one of the sensors employs some basic physical principle. Section 12 briefly describes how a broad range of sensors “work,” including all those in the kit. An entire science course could be built around this fascinating topic.

Credits

This guide is based upon work supported by the National Science Foundation under Grant No ESI-0624718. Any opinions, findings, and conclusions or recommendations expressed in this material are those of the author(s) and do not necessarily reflect the views of the National Science Foundation.

The author of this guide is Robert Tinker, the principal investigator for the ITSI project. Ed Hazzard contributed throughout to the pictures, construction ideas, data, and hot glue technology. Cynthia McIntyre reviewed and edited the guide. Trudi Lord scoured the Internet for the best possible collection of materials for the kit. Stephen Bannasch, Scott Cytaki, Aaron Unger, and Sam Fentress have created the fabulous software system used by ITSI. Carolyn Staudt, the project director, kept the entire team on target and under budget. Greg Collison (pictured at left) volunteered time to help us sort and pack the kits. Teachers and professional development experts have contributed many helpful suggestions and critiques. Thanks to all of you.

Section 1: Safety

Here are some rules that will keep you and your circuits safe.

1. Wear goggles with side protection. We don’t want wires accidentally getting in anyone’s eye.

2. Always disconnect from the computer before working on the Experiment board. This removes any chance of hurting the computer, the chips, or you.

3. Do not touch any part of the circuit when you are testing the circuit and it is connected to the computer.

4. Do not touch other fixed metal objects (like plumbing, a computer, or a metal chair) or any water, when your circuit is connected to the computer.

5. Do not use your fingers to remove chips. Many people have ended up with the chip embedded in their fingers. Use a small screwdriver instead, and gently pry the circuit loose from both ends. Actually, it is best to simply leave the chips in the Experiment board all the time. There is lots of room for them.

6. Before connecting a new circuit to the computer, have someone else check that it is correct. An incorrect circuit is no danger to you, but it could ruin kit parts.

7. Make neat circuits. A neat circuit is easier to check, to understand, and to modify. A rat’s nest circuit with lots of bare wires can cause errors. Two wires that are not supposed to touch can touch and burn out the interface circuit. Keep the leads short and insulate them with insulation that you have stripped off other wires, or use the heat shrink tubing.

8. Keep your work area neat. Keep unused materials stored away. A mess can lead to unexpected mistakes.

9. Until you are familiar with the DMM, never set it to read current. Don’t even rotate the switch past the current settings. It is easy to pass too much current through the DMM when it is set for current and this will burn out a fuse that protects the DMM but is a giant pain to replace. If your DMM suddenly seems to fail, it is probably because this fuse is burned out. The most common way to blow the fuse is to connect the leads to two ends of a battery or some voltage source as you would to measure voltage, but then switch to current. A very large current can flow—too much for your DMM. That’s why there is a fuse.

Know the Dangers and Non-Dangers

There is no way to be hurt by the low voltages in these circuits. The power used in our experiments is +5 volts derived from the computer. This is not an electrical danger, nor is there any danger from a properly working computer.

If the Experiment board is disconnected from the computer, it poses no electrical danger. This is why it should be disconnected unless in use. Disconnection also removes power from the Experiment board, so an incomplete or incorrect circuit cannot cause harm to the chips. Connect to the computer only when a circuit has been completed and carefully examined by someone else for errors.

The greatest electrical danger comes from a fault inside the computer that results in one side of the 120 V AC power main being connected to some part of the computer. A computer can still work in this condition but is a danger if the user touches a ground while touching the computer. A ground can be supplied by plumbing, metal on another computer or appliance, or water on the floor or sink. This applies as well to anyone using the computer or the Experiment board. So, in the unlikely chance that a computer has this kind of internal fault, never use the Experiment board while also touching a ground.

There is a danger to the chips, the temperature sensor, and the magnetic field sensor from static electricity. This is a major problem in the winter when the air is dry. Store the chips and sensors in conductive foam or a conductive plastic container (these are pink or metallic-looking). Before touching one, hold onto a ground with the other hand. Handle them as little as possible. Never put them in a pocket or other clothing unless they are inserted in conductive foam or conductive plastic. Do not confuse conductive plastic with regular plastic, which carries static charge and can zap a delicate circuit in a microsecond.

Section 2: Basics

This section covers basic electrical concepts. If you are stymied by electronics because you lack a clear understanding of the difference between voltage and current, or because you are not sure what a resistor does, this section is for you.

This section is designed to help sort out current, voltage, resistance, and some basic concepts that will be used over and over. If you are just a beginner, you may want to skip the last two topics. If you are familiar with the basics, you might find useful information in these parts.

Charge

Electronics is all about controlling and detecting the movement of charges. The most prevalent charged object in electronics is the electron. Electrons are tiny, 1/2000 the mass of hydrogen, the lightest element. Each electron carries one unit of negative charge, called the elementary charge. Because it is charged, an electron tries to get away from anything charged negatively and is attracted by anything charged positively. Since the nucleus of every atom contains positive protons, electrons are strongly attracted to them, forming electron shells.

In metals, each atom contributes one electron that is free to roam throughout the metal, much like gas molecules are free to roam around a room. Because electrons are so light, they move easily and quickly in response to external electrical fields. This is why metals conduct electricity. The atoms in insulators, on the other hand, hold on to their electrons and don’t let them roam, so charge cannot flow through them.

If you could collect 6.24x10¹⁸ electrons in one place, you would have a coulomb (C) of charge, the standard measure of charge. There are about 1,500 C of free electrons in a gram of copper, so one coulomb does not sound like much. But you will never find even the slightest fraction of a coulomb in one place without some balancing charges. The attractive force of one positive coulomb and one negative one separated by a meter would be almost equal to the weight of a million metric tons!

The symbol Q is traditionally used to stand for the amount of charge something has in coulombs, and the symbols q or e are often used stand for the elementary charge, which is 1.6 x 10^-19 C.

Sometimes, there is a slight charge imbalance. If you rub two different insulators, a tiny bit of charge can be transferred from one to the other. “Static cling” is an example of this. Other examples include the shock you get after walking across a rug in the winter, or lightning caused by water drops falling through air. All these effects are due to miniscule fractions of a coulomb.

Electrons can flow through a wire, because their negative charges are exactly balanced by the positive charges on the copper atoms that donated the electrons in the first place.
As a result, the wire is everywhere neutral. If, by some chance, electrons happen to bunch up in one place, they will upset the charge balance, making that part slightly negative, which will send the extra electrons fleeing until perfect neutrality results.

The extreme force caused by any charge imbalance explains why charges only flow in complete circuits. If you pull a coulomb of electrons out of one end of a wire, you must arrange for a coulomb to flow in the other end to keep the charge balance. If none can flow in the far end, you cannot pull the electrons out the near end and no charge will flow.

Electrons in metals are not the only source of charge in electronic circuits. Ions are atoms that are not neutral, having either too many or too few electrons in their electronic shells. In a liquid, ions can drift in response to electric fields, just like electrons do in a wire. This is why salt in water will conduct electricity. Ions are much bigger that electrons and in solution they are surrounded by a snowball of frozen water, so they move much more slowly than electrons. Ions can be made from a gas, too, and they also carry charge. This is what happens in a fluorescent light. In semiconductors electrons are lightly bound to atoms so they are insulators, but light, temperature, or impurities can jog the atoms enough to create in a few roaming electrons, making them conductors. This is why substances made from these atoms are called semiconductors. Sometimes the hole left by a roaming electron can move around, too, acting like a positive charge.

Current

Electrical current is the flow of charge. Imagine you wanted to find out how much current was flowing in a wire. You could cut the wire and insert a tollbooth where you would count the number of electrons that zoomed by. If you counted the number of electrons in a second you would be measuring the current. Current is measured in amperes (A). One ampere is a coulomb of charge flowing every second. The symbol usually used for current is I.

An ampere (or amp for short) is a large current, so milliampere (mA) is often used in electronics, for 1/1000 of an ampere. In some experiments, we will actually deal with a microampere (µA), which is a millionth of an amp, and a nanoampere (nA), which is one-billionth of an amp.

Benjamin Franklin did a lot of experiments with electricity and made a guess that current was actually something with a positive charge flowing from plus to minus. Since his time, that has been the definition of current—the flow from positive to negative.

Now we know a lot more and realize that current is usually negative electrons flowing from minus to positive. This creates a lot of confusion, because Franklin got it backwards. So, we cling to the idea that current flows from positive to negative. This is sometimes called conventional current to distinguish it from the actual electron flow, which goes from negative to positive. Thanks a lot, Ben.

Voltage

Voltage is a kind of electrical pressure that can cause charge to flow. A positive charge such as a positive ion will flow from a higher voltage to a lower voltage. A negative charge such as an electron, with flow the other way, from a lower voltage to a higher one. The conventional symbol for voltage is V. Voltage is measured in volts.

At the atomic level, a negative voltage can be produced by increasing the concentration of electrons, squeezing them together slightly. A positive voltage is the opposite; it can be made by removing a few electrons, making them slightly less dense. If one end of a wire is positive and the other negative, electrons will move from the negative end where there is more of them, to the positive end where there are fewer. This flow constitutes a current. This current will flow until there is no voltage difference.

We don’t normally talk about the density of electrons, because it does not change much. In the discussion under “charge” above, we emphasized how much force is caused by the slightest imbalance of charge. Because of this, the tiniest difference in electron density causes huge forces that push the electrons to neutralize any difference. For example, to raise the voltage of a 20 cm diameter copper sphere to 1,000 volts would only require 10^-9 C or about 5 billion electrons. That sounds like a lot, but if the sphere were solid it would contain 4x10²⁰ free electrons so only one extra one for every 400 billion would be required to generate 1,000 volts. Our circuits will be limited to 5 V, so the electron density differences we will encounter are even less.

Voltage and energy are closely linked. It requires energy to push extra electrons into a region to give it a negative voltage. It also requires energy to pull electrons out of a region to make it positive. Thus, a voltage difference represents a potential energy difference. For this reason voltage is sometimes called “potential.” The energy can be turned into other forms by letting the charges flow until there is no voltage difference.

By definition, one joule of energy is released with a coulomb of charge flows through a voltage difference of one volt. Similarly, it requires one joule to force a coulomb of charge to gain one volt of energy.

Voltage is always measured as a difference between two parts of a circuit. It is a measure of the amount of energy that would be released if a coulomb could flow from one point to the other. It makes no sense to assign the voltage of one point in a circuit. A voltage is always measured as a difference between two points, or “relative to” some point.

A similar situation happens with gravitational potential energy. A ball on a table does not have a unique potential energy. Relative to the floor it has a positive potential, but relative to the ceiling it has a negative one.

In circuits a “ground” point is often assigned to part of a circuit and all voltages are measured relative to that point. The ground may or may not be electrically connected to the earth; that is not the point. The ground is really just the reference for voltage measurements, much like you might define the floor of your room as the reference for all gravitational potential energy measurements in your room. So, if there is a ground, people will say things like: “This point is at 2.5 volts.” That is shorthand for saying: “The voltage difference between this point and ground is 2.5 V.”

Resistance

Resistance is a measure of how difficult it is for charge to flow. A voltage is always required to make charge flow, but how fast charge flows through a circuit depends on the resistance of the circuit. If there is a large resistance, the amount of current will be small. Conversely, if the resistance is small, the current will be large.

The usual symbol for resistance is R and its units are ohms (Ω). One ohm is a volt per ampere. The resistance of a part can be measured by applying a voltage V across it and measuring the resulting current I. In symbols,

R = V/I

This equation is known as “Ohm’s Law.” Not all electronic parts obey this equation, so it isn’t much of a law. Suppose you had an unknown electronic component and you repeated the measurement of current for a range of different voltages. If you got the same value for R in each case, your component would be called “ohmic” because it does obey Ohm’s Law. If you tried this with a light bulb, motor, or LED, for instance, you would find that they are not ohmic.

Resistors are ohmic. They are handy components that are used throughout electronics to restrict the flow of current. The ITSI kit has resistors with valued from 1 Ω to 1 MΩ (that’s 10⁶ ohms!). The amazing thing is that they are all the same physical size, even though their resistance is so different. Inside, they are made from a mix of clay and carbon in the form of graphite. By changing the concentration of graphite, these huge differences can be obtained in the same space.

The symbol for a resistor is shown at right.

Resistors have color bands that indicate their value. For information about reading these bands, see http://en.wikipedia.org/wiki/Resistor. There are several toosl on the web that convert the colors to values, such as http://www.dannyg.com/examples/res2/resistor.htm.

Capacitance

Capacitors store charge. They consist of two conductive surfaces separated by an insulator. The symbol for a capacitor reflects this structure. It is shown at right.

Charge flows into a capacitor on one lead to one surface. This induces the opposite charge on the other surface, which can happen only if charge flows OUT the other lead. So, from the outside, it looks like charge flows through the capacitor, even though there is no connection between the leads. Because there is no connection, the flow cannot continue indefinitely. As more and more charge flows in one side, the charge density goes up, causing a voltage that opposes more flow. So, if you attach a capacitor to a voltage source, some amount of charge will flow in and then it will stop flowing. The ratio of the charge Q that will flow into a capacitor to the voltage V that causes the flow is the capacitance C. As an equation:

C = Q/V

The units of capacitance are farads (F). A capacitor that can store one coulomb when one volt is applied would have one farad of capacitance.

The capacitor at right has a capacitance of 220 µF, or 2.2x10^-4 F, which is relatively large. Useful capacitors can be as small as a few picofarads; the largest ones can be 1 F, but that is unusual.

The 16 V printed on this capacitor indicates that no more than 16 V can be applied to it, or it will fail.

A capacitor that has a plus and minus side is “polarized.” The capacitor pictured is polarized. The rectangle on the top is supposed to be a minus sign to indicate which lead is minus. The nearest lead must be always kept more negative than the other lead or the capacitor will fail. The plus lead is longer than the minus one, too. Some capacitors have a plus sign instead and the minus.

There are several kinds of capacitors. Some are polarized like this one, whereas others are not. If a capacitor is polarized, its symbol includes a plus sign on the side that must be positive. Symbols for polarized capacitors are shown at right. The left-hand one is better because the other can easily be confused with a battery.

Inductance

[There are no inductors included in the ITSI kit. This page will be supplied later for completeness. ]

Equivalent Resistance

The idea of “equivalent resistance” is that a component or group of components act as though they are created from other components. The concept is quite helpful in analyzing and simplifying circuits.

The simplest equivalence is that of two resistors in a row are equivalent to one that is the sum of the two:

A battery is a source of voltage. Most common batteries generate about 1.5 V, but there are many other voltages possible. A battery is represented by two parallel lines, one of which is longer, representing the positive terminal. This same symbol is used to represent a voltage source that is equivalent to a voltage, but may be something else.

No battery can supply a very large current at its rated voltage. The voltage will drop if it is called on to supply a sufficiently large current. This is often represented as the equivalent circuit to the right. The symbol on the left is represents a perfect voltage source that can supply an infinite current at voltage V. The resistor R is not really part of the voltage source, but it accounts for the fact that it is not perfect. The output voltage of this real source V_out when it is supplying a current I, is V minus IR. In other words, the actual voltage produced by this real battery is reduced by the IR voltage drop through the equivalent resistance R. It will output the ideal voltage V only when it not asked to provide any current! R is sometimes call the output resistance. The bigger and fresher the battery, the smaller R will be.

A voltage meter measures the voltage between two points. It is symbolized as a circle with a “V” in it. This is also the symbol for an ideal voltage sensor, one that senses a voltage difference without drawing any current. It is impossible to create an ideal voltage sensor; they always require a bit of current. A real voltage sensor has the equivalent circuit shown at right. There may not really be a resistor connected across its terminals as shown, but it acts as though there is one. When this real meter is connected to a voltage difference V, it will draw a little current, equal to V/R.

The equivalent resistance R is called the input resistance. For a very good voltage detector such as the digital meter, the input is quite high, 100 MΩ or more, so not much current is required.

Matching Outputs and Inputs