2024 Notes

Busy time for TAs, lots going on. Meter issues: “giving weird readings”

   Gotta get folks in the habit of marking faulty equipment w/ tape

Many dead bulbs: they're rated for 12V at 250 mA Some LEDs were backwards

   This is in the lab manual, but people didn't read it.

Circuits I: Electrical Measurements

While originally used to describe metallic wires, the relation known as Ohm's law has proven useful for describing the behavior of many materials. This principle was discovered in 1827 by Georg S. Ohm (1787 - 1854) and is the basis of many essential facts in practical electricity. It relates the current $I$ through a component in an electrical circuit to the potential difference $V$ across that element and to the resistance $R$ of the component as

$V = IR$. $(1)$

Current is typically measured in amperes ($\text{A}$), potential difference is measured in volts ($\text{V}$), and resistance is measured in ohms ($\Omega$).

There exists a large class of materials where the value of $R$ is found experimentally to be independent of $V$ and $I$. In such a case, Eq. (1) is a very simple linear relation between the current through and the voltage across the element. Such elements are ordinarily called resistors, symbolized as shown in Fig. 1. They are said to be linear or ohmic devices.

Figure 1: Symbol for a resistor

Today, there are many components or chips that rely on semiconducting materials, which cannot be assigned a static value for resistance. The entirety of digital computing is made possible due to such compounds, so substances that don't obey ohm's law can be as important as those that do. Furthermore, some substances may have resistances that depend on other physical properties, such as their temperature, illumination, or strain. These are what physicists typically end up needing knowledge of electronics for, as turning physical properties into electrical signals makes it much easier to record and measure important physical processes.

Objective

  • Familiarize yourself with the concepts of electrical potential, current, and resistance, and explore a model of how they relate to one another.
  • Gain experience with instrumentation and basic circuit building, and develop intuition on how measurement devices work.
  • Learn about the important voltage divider circuit and how such a circuit can be used to create a sensor.

Introduction


An analogy

As you'll discover throughout this course, electrical potentials and currents are ubiquitous in the study of electromagnetism. In fact, they are all around us: inside the circuitry that powers the computer through which you are reading this, in the wall, in medical probes and machinery, in our bodies, etc.

But what is this potential and how can we use it to make measurements and do useful things? For many cases, it turns out that it is not so different from the gravitational potential that you studied last quarter. In that case, we defined the gravitational potential due to the mass of, say, a planet such as Earth, to be zero at infinity and found that objects tend to move from regions of higher potential to lower potential; that is, objects experience an attractive gravitational force between them.

Consider for instance a mountain with a river flowing down from its peak. From our studies on gravity, we know that, the higher the peak, the higher the potential that the water experiences at the top relative to sea level will be. We also know that the force due to gravity that pulls the water down the river is proportional to the mountain's slope, such that the river's flow rate, or current, will be proportional to the potential difference between two points on the mountain.

Now, what if there is an obstruction such as a bunch of boulders in the river? Naturally, the flow rate will decrease since there will be some resistance to the current due to the obstruction the boulders provide. If we put a turbine-powered generator somewhere in the path of the river, we will see that the power output of the generator will depend both on how many boulders there are and on the size of the turbine (which is essentially a collection of movable boulders). We could continue analyzing this system, but let's leave the details for the hydroelectric engineers.

The above analysis applies in many respects to an electrical circuit. Instead of height differences, we have voltage differences; instead of water, we have electrical charge inside metals; and instead of turbines and boulders, we have elements through which charge flows – including the metal itself. Of course, there are many other complications, some of which we will explore during this lab, but the analogy serves as a good starting point to thinking about circuits.

Experimental procedure 


Getting started

Circuit diagrams

In past labs, you have seen a number of circuit diagrams. These diagrams differ from many other illustrations used in physics because they do not depict the physical state of the circuit. Instead, they are a blueprint for how to electrically connect components. We will look a bit more carefully at such diagrams today.

Connecting circuits

To prevent blowing fuses in power supplies and meters, please use the following steps when connecting circuits:

  • Turn off the power supply.
  • Connect the circuit. For clarity, connect series loops first, then add sections in parallel (e.g., voltmeters). Follow wiring diagrams point by point as you connect the circuit.
  • Select the meter function (current, voltage, resistance, etc.).
  • Turn on the power supply and increase the voltage slowly.

Resistor values

Many resistors are marked with colored bands which indicate their resistance values and tolerance. The bands are to be read starting closest to the end of the resistor as shown in Fig. 2.

Figure 2: Resistor color code

The digit values represented by each color are shown in Table 1. The tolerance values represented by each color are shown in Table 2.

Digit Color
0 Black
1 Brown
2 Red
3 Orange
4 Yellow
5 Green
6 Blue
7 Violet
8 Gray
9 White
Table 1: Digit values
Tolerance Color
2% Red
5% Gold
10% Silver
20% None
Table 2: Tolerance Values

For example, if the colors are red, orange, yellow and silver, then the resistance is $R = 23\times 10^4\text{ \(\Omega\)} \pm 10\%$ or $230\text{ k\(\Omega\)}$. 

If there were three bands that were brown, black, and brown, then the resistance would be $R = 10\times 10^1 \text{ \(\Omega\)} \pm 20\%$ or $100\text{ \(\Omega\)}$.

Lab notebook template

One member of the group should click on the link below to start your group lab notebook. (You may be asked to log into your UChicago Google account if you are not already logged in.) Make sure to share the document with everyone in the group (click the “Share” button in the top right corner of the screen) so each member has access to the notebook after you leave lab.

Practice with multimeters

Using the multimeter

Making electrical measurements is a bit different than most of the other types of measurements we've done. Using a ruler to measure a length won't change something's length, nor will weighing an object with a scale change its mass. But, using a multimeter can change how a circuit behaves if we're not careful. Thus, if you're seeing something on a meter that you don't expect, double check that the correct terminals are attached to the circuit.

Take a look at the generic multimeter shown in Fig. 3. One wire should always be connected to the common (COM) terminal, and the other will be attached to one of the following:

  • “$\mathrm{V}/\Omega$“ for measuring any voltage or any resistance;
  • “$200 \text{ mA}$” for measuring a small current; or
  • “$10\text{ A}$” for measuring a large current.

For measuring voltages, you'll connect the meter to either side of a component (i.e. in parallel).

For measuring currents, you'll connect the meter in-line with the component (i.e. in series).

For measuring the resistance (of a static device like a resistor), you'll connect the meter directly to either side of the component (with nothing else connected in the circuit).

Finally, you'll need to set the dial to what you want to measure. The tilde ~ indicates an AC value (not used today), whereas the straight & dashed line combination indicate DC values.

Figure 3: Depiction of a generic multimeter. Your version may have a different layout, multiple settings for each measurement type, or other features.
What's in my multimeter?

The specifics of how a modern multimeter works are beyond what we can teach in an introductory physics course. However, we can make a first order model for how we expect it to behave, as follows:

Note that the small resistance for current measuring mode are crucial since we want to change our circuit as little as possible when we attach our meter. To measure current the meter must be in series with other elements, and thus a small resistances make the most sense.

Likewise when measuring voltages we attach the meter in parallel with a component or branch, and by having a large resistance between the leads we ensure that this doesn't impact the behavior of the rest of the circuit much.

Measuring direct current (DC)

Using a resistor value between $1\text{ k\(\Omega\)}$ and $10\text{ k\(\Omega\)}$, set up the circuit in Fig. 4.

Figure 4: Current measurement
  • Plug the black test lead into the “COM” jack on the multimeter and the red test lead into the “$\text{mA}$” jack. Set the function of the digital multimeter to be an ammeter.
  • Set the large current limit knob on the power supply to 0.2 A and set the smaller current limit knob fully clockwise.
  • Turn on the power supply and observe the meter. If the reading is negative, you may have connected the circuit differently from the diagram. Check it.
  • Adjust the power supply and observe and record the range of currents. Turn off the power supply.
Help! I'm not seeing any current!

There are a few reasons you might not be seeing a current in your circuit. 

To start, make sure that your meter is on the current setting (i.e. the dial is turned to $\text{mA}$) and that the leads are in the correct socket. If this is the case and you're still seeing nothing, the fuse in your meter may be blown.  Here's how to check:

Connect one meter in resistance mode to the other in current mode, as shown below. If the meter being tested reads $0.1$ to $0.2\text{ mA}$ and the other reads a couple of ohms, then the fuse is fine.

If, as shown below, the meter being tested reads $0\text{ mA}$ and the other reads overload (O.L) then the fuse is probably blown. Fortunately, replacing them is easy.

I need to replace my meter's fuse

There should be a plastic container with several screwdrivers and spare fuses in your lab room, ask your TA where it is if you can't find it.

First, turn over your meter and remove the screws that hold it closed with a Phillips (+ shaped) screwdriver.  Don't worry if there's only one screw, many of our meters are left like that to make changing the fuse easier.

Next find the $500\text{ mA}$ fuse, which should be labeled both on the board and on the fuse itself. Some fuses have solid white bodies, whereas others have glass bodies with a thin wire inside. Either way, they work the same way.

Pop out the old fuse and replace it with a new one. A flathead screwdriver can be useful here. If you want to be extra certain that the new fuse is good (and that the old one is bad) use a different meter to test its resistance. It should read a couple of ohms, any more and the fuse is no good.  

Close your meter back up and test it to make sure it works. The dead fuse can be thrown away; there's nothing hazardous about them and they can't be fixed.

Simultaneously measuring DC voltage

Using the same circuit as above with the power off, add a voltmeter across $R$ as in Fig. 5.

Figure 5: Simultaneous measurement of current and voltage
  • Since the maximum voltage possible from the power supply is $50\text{ V}$, set this second meter to read DC volts.
  • Plug the black test lead into the “COM” jack and the red test lead into the “$\text{V}$” jack.
  • Turn on the power supply. If the reading is negative, check the circuit.
  • Adjust the power supply and observe the range of voltage available.

Keep this circuit set up; you'll be using it for the next part.

Testing conductive materials

Now that you have a bit of practice with the meters, you'll use them to test the behavior of a few different conductive elements. For each element, you will vary the power supply voltage and measure the voltage across the element along with the current through it. If a material is Ohmic, then a plot of the voltage versus current ($V$ vs. $I$) should be linear; if it is not Ohmic, then the curve will have a different shape. As you test, remember that you can reverse the connections from the power supply to produce negative voltage differences to see if the element behaves differently when the direction of the current flow is reversed.

Produce voltage versus current plots for the following elements:

A resistor
A light bulb
An LED (Light Emitting Diode)

(This is actually an LED in series with a resistor, which helps keep us from damaging the diode)

We provide a Google Colaboratory notebook running Python code which you use to plot your data. Record measurement values in your lab notebook, and then enter them here to visualize how current and voltage relate to each other for each element.

In your lab notebook, show your plot for each element and include a brief description of what you observe for the ones that emit light. (If your resistor emits light, you've done something terribly wrong.) Which elements are Ohmic and which are not?

Circuit elements in series and parallel

Next, you'll practice connecting multiple elements together in different configurations.

Resistors in series

  • Choose two resistors, measure their resistances individually, and then connect them in series as in Fig. 6.
  • Using the resistance values for each resistor measured earlier, calculate the expected total series resistance.
  • For one setting of the power supply, measure $V$ and $I$ and determine the total resistance.
Figure 6: Resistors in series

Resistors in parallel

  • Connect your resistors and the meters in the circuit shown in Fig. 7.
  • For one setting of the power supply, measure $V$ and $I$ and determine the total resistance.
Figure 7: Resistors in parallel
Can something be connected neither in series nor in parallel?

Yes! Consider the three elements connected together as follows:

Resistor $\text{A}$ can't be in parallel with $\text{B}$ or $\text{C}$ (it only shares one common connection with them).  Nor can it be in series with just resistor $\text{B}$ or $\text{C}$; the current through $\text{A}$ is split between $\text{B}$ and $\text{C}$. More advanced techniques are used to analyze the behavior of such networks.

Voltage division

Now we'll do something that is ubiquitous in electronics: dividing voltage. In some cases, this is done so that different things can be powered by a single battery. In other instances, voltage dividers form the basis of sensors that connect physical properties (like position) into electrical properties (like voltage).

Here we'll introduce the notation of a voltage input $V_{\text{in}}$ and a voltage output $V_{\text{out}}$. For the purposes of this class $V_{\text{in}}$ will usually denote a voltage from a power supply, and $V_{\text{out}}$ will denote where to measure a voltage to determine the effect of the circuitry.

Does current go from in to out?

Not necessarily. If there's no meter or other circuit attached to the $V_{\text{out}}$ connections, then having a current there would imply that electrons were flying off of or on to the wires. Voltages can exist without currents. For example, a battery on a shelf has a fixed voltage across the terminals even though no electrons are moving.

Fixed voltage divider

Connect the circuit shown in Fig. 8. Be sure that both meters are on the DC voltage setting. This circuit is useful when a fixed fraction of some input voltage is needed.

Figure 8: Voltage divider

From Ohm's law and how resistors add in series, it can be shown that

$V_{\text{out}} = \dfrac{R_2}{R_1+R_2}V_{\text{in}}$. $(2)$

For one power supply setting, measure the input and output voltages to test the above relation for your circuit.

Replacing $R_2$ with an element whose resistance depends on some physical quantity (e.g. temperature, pressure, light) is a way of making a basic sensor.

Slide-wire potentiometer

  • Keep $V_{\text{in}}$ from the supply around $10\text{ V}$ or $20\text{ V}$ or so. Any higher, and you'll soon be smelling burning wood!
  • When using the ammeter, you will now be measuring currents up to 2 A, so make sure to change your ammeter wiring to use the “10 A” input on the meter instead of the “mA” input. If you do not, you will blow the small fuse inside your meter!
  • Adjust the current limit knob on your power supply to 2 A (and again, make sure the smaller current limit knob is turned fully clockwise).

 A variable voltage divider can be made by replacing the fixed resistors with a length of resistance wire and a sliding contact as shown in Fig. 9.


Figure 9a: Slide-wire potentiometer

Figure 9b: Schematic circuit diagram of potentiometer

For this setup, you'll test the effect changing the sliding contact has on the output voltage $V_{\text{out}}$. If the wire is uniformly made, then the resistance across a portion of it is proportional to length. Using this with Eq. (2), we can find the relation:

$V_{\text{out}} = \dfrac{L_2}{L_1+L_2}V_{\text{in}}$. $(3)$

Keeping $V_{\text{in}}$ constant, test this relationship and record your results (along with a plot) in your notebook.

Creating practical sensors

Since the currents for the rest of the lab will again be relatively low, change your ammeter wiring back to the “mA” input instead of the “10 A” input and return the current limit knob on your power supply back to 0.2 A.

Now that you've seen how a fixed voltage divider and an adjustable voltage divider work, it isn't too large a leap to translate these concepts into a practical circuit. If one of the resistors is fixed and the other one is allowed to vary (either from a mechanical response – like turning a knob – or from a physical response – like reacting to light or pressure), then the output voltage of the divider circuit will change in response.

For example, we can create a dimmer (for a light) or a volume control (for a speaker) by making one resistor into a variable resistor that the user controls. As the resistance changes, the voltage to the light or speaker changes as well.

Or, conversely, we can use a variable resistor that reacts to an external stimulus and then monitor the output voltage of the divider. Suppose, for example, that we had an object whose resistance changed as the light intensity changed; as the voltage output increased or decreased, we could use these values as a sort of light intensity meter. Or, suppose we had a resistor that responded to pressure; in this way, we could create a weight scale.

Light sensor

Return to the fixed voltage divider circuit diagram, Fig. 8. Replace resistor $R_2$ with one of the photoresistors.

A CdS based photoresistor. You may have seen these in night lights.
  • As you cover/uncover the resistor or as you shine light directly on it (either from the provided lamp or from the flashlight feature on your cell phone), how does your output voltage respond? (Be as detailed as you can be!)
  • Is your circuit sensitive enough to tell when a light is on or off? Could you use as a light intensity meter?

Scale

Next, replace $R_2$ in your circuit with the piece of Velostat (a pressure-sensitive material).

  • How does the output voltage respond as you push on the material? (Be as detailed as you can be!)

Using the provided masses, make measurements of your output voltage as a function of mass placed onto the pad.

  • How could this device be used to make a weight scale?

Creating a dimmer switch

Now that you've seen how a fixed voltage divider and an adjustable voltage divider work, it isn't too large a leap to translate these concepts into a practical circuit like a dimmer knob (for controlling the brightness of a light) or a volume knob (for controlling the loudness of a speaker).

In such a case, all we need to do is replace one leg of the voltage divider with our device (the lamp or the speaker) and replace the other leg with a variable resistor.

An example of a common type of variable resistor – called a rotary potentiometer – is shown in Fig. 10. This device works like the slide wire above, but is rolled up into a more compact form. The total resistance between the first and third legs is fixed, but as you turn the knob, the resistance between the first and second legs (or between second and third legs) changes. In this way you can select any resistance between zero and the maximum value.

Figure 10: A potentiometer. The total resistance between the first and third legs (Green & Orange) is fixed, but as you adjust the knob, the resistance between the first and second legs (or second and third legs) changes (Purple to Orange or Green to Purple)

Turn the fixed voltage divider circuit above (Fig. 8) into a lamp dimmer circuit and chose an input voltage of $V_{in} = 50\textrm{ V}$.

  • Use a 1k$\Omega$ potentiometer (connected between first and second legs) in place of $R_1$.
  • Use the light bulb in place of $R_2$.

How does the lamp behave as you adjust the potentiometer? Is it brightest when the potentiometer is close to zero ohms or close to 1k$\Omega$?

Using the tools at your disposal – voltage measurements, current measurements, direct resistance measurements, your voltage versus current plot for a lamp from the start of the lab, and Eq. (2) above – determine the “effective resistance” $R_2$ of the lamp at the following points:

  • When $V_{out}$ is at a minimum value.
  • When $V_{out} = (1/2)V_{in}$.
  • When $V_{out}$ is at a maximum value. (HINT: at this point Eq. (2) is no longer useful. Even for a non-ohmic device, we can still say that for a given value of voltage and current, the “effective resistance” at that point is $R = V/I$.)

Submit your lab notebook

Make sure to submit your lab notebook by the end of the period. Download a copy of your notebook in PDF format and upload it to the appropriate spot on Canvas. Only one member of the group needs to submit to Canvas, but make sure everyone's name is on the document!

When you're finished, don't forget to log out of both Google and Canvas, and to close all browser windows before leaving!

Post-lab assignment


Answer the questions/prompts below in a new document (not your lab notebook) and submit that as a PDF to the appropriate assignment on Canvas when you are done. You should write the answers to these questions by yourself (not in a group), though you are welcome to talk to your group mates to ask questions or to discuss.

Conclusions

The conclusion is your interpretation and discussion of your data.

  • What do your data tell you?
  • How do your data match the model (or models) you were comparing against, or to your expectations in general? (Sometimes this means using the $t^{\prime}$ test, but other times it means making qualitative comparisons.)
  • Were you able to estimate uncertainties well, or do you see room to make changes or improvements in the technique?
  • Do your results lead to new questions?
  • Can you think of other ways to extend or improve the experiment?

In about one or two paragraphs, draw conclusions from the data you collected today. Address both the qualitative and quantitative aspects of the experiment and feel free to use plots, tables or anything else from your notebook to support your words. Don't include throw-away statements like “Looks good” or “Agrees pretty well”; instead, try to be precise.

REMINDER: Your post-lab assignment is due 24 hours after your lab concludes. Submit a single PDF on Canvas.