# ATAT 105 Basic Electricity
> # [[T105 Week 3| ◀️ ]] [[T105 Home| Home ]] [[T105 Week 5| ▶️ ]] [[QR T105 Week 4| 🌐 ]]
># [[T105 Week 4|Week 4]]
>- [[T105 Week 4#Ohm's Law|Ohm's Law]]
>- [[T105 Week 4#Series Circuit|Series Circuit]]
>- [[T105 Week 4#Calculating Values in a Circuit|Calculating Values in a Circuit]]
># [[T105 Week 4#Lab|Lab]]
>- [[T105 Week 4#Ammeter]]
>- [[T105 Week 4#Measuring resistance]]
>- [[T105 Week 4#Measuring voltage]]
>- [[T105 Week 4#Measuring current]]
>- [[T105 Week 4#Measure across an open]]
>[!jbplus|c-blue]- Lesson Intro
>### What
>In this lesson you will learn some laws that will allow us to organize some of the discoveries we have made in the past weeks to that we can understand more deeply and thoroughly the properties of electrical circuits.
>
>### Why
>
>The relationships between voltage, current and resistance and the mathematical calculations that allow us to derive values in a circuit will be used in the electrical lab, and when troubleshooting avionics or electrical snags.
>### Approach and Objectives
>
>By understanding the following topics, you will have achieved the learning outcome for this lesson. Consult your course outline for the learning outcomes and other details of this course.
>
>#### Course Learning Objectives
>
>- CLO 10. Assemble a functional electrical circuit using components according to a given circuit diagram.
>- CLO 11. Show using a Digital Multimeter (DMM) the measurement of voltage, current and resistance in a circuit.
>
>### Testing
>
>You will be tested on this material on Assignment 2, the Midterm, and the Final Test, as per the [[T105 Intro#Testing and Grades|testing strategy]].
>[!jbplus|c-blue]- Prof
>### Objectives
>
>This week we tie a lot of things together under Ohm's Law. This is an important milestone, as by the end of the lesson, the student will know the voltage, current and resistance at any point in the circuit.
>
> ### Theory
>For the theory course, the laws, and then how to use and manipulate their formulae. A full walkthrough is done, don't be afraid to repeat yourself according to student comprehension. Calculators out!
>### Lab
>For the lab, calculate and measure, which will be a very common mode. This supports the idea that they must have an idea what to expect before they measure, or the measurements make no possible sense. Measuring current is new, and a good suggestion is to have them raise their hand when they are about to measure current. If they understand, it's a 5 second check. If they don't, it's a good time to get them straight on the rules, including spotting parallel paths.
## Ohm's Law
As discussed earlier, a quantity of electrons produces an electromotive force that causes electrons to flow through a circuit.
However, as electrons flow through a conductor, they are met by an opposition or resistance.
By assigning values to the force, flow, and opposition within a circuit, the relationship that exists between these items becomes apparent.
### Ohm's Law as a Formula
>Ohm's Law states that the current that flows in a circuit is directly proportional to the voltage (force) that causes it, and inversely proportional to the resistance (opposition) in the circuit.
- The symbol used for current is I
- The symbol used for the voltage is V (or E for electromotive force)
- The symbol used for resistance is R
![[Pasted image 20210926125201.png|Ohm's Law]]
Refer to [[T110T SSGW05#Formula Relationships|ATAT110]] to remind you how to manipulate formulae. Try to derive the three Ohm's Law formulae yourself before revealing the answer:
V = ?
I = ?
R = ?
[[A Ohms Law|🅰]]
### Ohm's Law Examples
We have a 6 V battery driving a lamp with a filament resistance of 3 ohms. Calculate the current:
I = V/R = 6/3 = 2A %%latex%%
![[Pasted image 20210808124333.png|350]]
Lets say we replace the 6V battery
with a bigger one of 12V. How does the current change?
![[Pasted image 20210808124508.png|350]]
[[A Ohms Law 2|🅰]]
Often we will have information available to us, but this information could change. Armed with Ohm's Law, we continue:
Suppose we have a 6V battery driving a lamp and we are getting a current of 3A. Calculate for resistance:
![[Pasted image 20210808124926.png|350]]
[[A Ohms Law 3|🅰]]
One last example. We have a battery driving a
lamp of 10Ω and we measure a current of 1.2A. For some reason, our voltmeter is not working. So, calculate for voltage:
![[Pasted image 20210808124944.png|350]]
[[A Ohms Law4|🅰]]
## Series Circuit
A series circuit is a circuit where there is only one path for the current to follow. All of the circuits you have built so far have been series circuits.
All of the electrons flow in the same direction through the circuit and follow the same path.
![[Pasted image 20210808125209.png|350]]
This leads us to two rules or laws that apply to series circuits.
![[Pasted image 20210808125341.png|350]]
### Kirchoff's Law of Voltage
All of the voltage from our source (battery or power supply etc.) MUST be used up in the circuit.
So, if 6V is applied to the circuit, the total of all the voltage drops in the circuit must add up to 6V.
Kirchoff's Voltage Law states
>The algebraic sum of the applied voltage and the voltage drop around any closed circuit is equal to zero
What this means is that you can't "lose" any voltage.
![[Pasted image 20210808125703.png|350]]
Voltage law 6V - 3V - 3V = 0
Ideally, you are thinking back to previous labs where we demonstrated this without explanation. Check your notes etc, and verify that every time you measured the voltage of all the loads combined, (lamp, lamp and resistor, etc) you measured the same voltage as the supply.
### Kirchoff's Law of Current
In a series circuit the current will be the same everywhere in the circuit.
Kirchoff's Current Law states
>The algebraic sum of the currents at any junction of conductors in a circuit is equal to zero
What it really means is you can't "lose" any current. If a certain amount of current comes into a junction (such as the lamp) the same amount of current will leave it. If you look at the entering as adding, and the leaving as subtracting, you see where the zero sum comes in.
What goes into the circuit must come out of the circuit.
![[Pasted image 20210808125840.png|350]]
### Calculating Resistance in a Series Circuit
In order to know the current flow in a series circuit we need to know how much resistance the circuit contains.
>The total resistance in a series circuit is the sum of each of the individual resistances in the circuit
$R_T = R_1 + R_2+ R_3 + R_4 + ...$
![[Pasted image 20210808130008.png|350]]
If a circuit has 3 resistors with values of $10\Omega$, $20\Omega$, & $30\Omega$:
$R_T= 10\Omega + 20\Omega + 30\Omega = 60\Omega $
![[Pasted image 20210808130225.png|350]]
Once we know any two values for volts, amperes, or resistance we can calculate the third using Ohm's Law and its derivative formulas.
![[Pasted image 20210926125201.png|Ohm's Law]]
### Voltage Dividers
Last week we built this circuit:
This is called a voltage divider because it divides the total voltage. This voltage can then be wired to another circuit elsewhere.
According to Kirchoff:
$V_T = V_1 + V_2 + V_3$
That also means that the voltage at point B = V<sub>2</sub> + V<sub>3</sub> and that the voltage from point A to point C is equal to V<sub>1</sub> + V<sub>2</sub>.
![[Pasted image 20210808131157.png|350]]
This week we will build the same circuit, but now we will see that we have a much deeper understanding of what is going on electrically, and the effects of each and every component in the circuit.
## Calculating Values in a Circuit
Here we bring together a number of details, including skills you are learning in [[T110 Home|ATAT110]] to calculate all values in a circuit. We will treat this as a little puzzle, and observe how you must piece together the available evidence and clues in order to solve the puzzle. [[Ohms Law in Circuit Analysis|🎞️]]
Given this circuit, calculate all other values and fill in the table.
- Note the labels of the values. Double numbers mean that two components are being measured.
- The subscript T refers to the total of whatever unit of measurement is in the entire circuit.
- Use the symbols and abbreviations for your values. If you do not, you will have a bunch of numbers on the page, and errors will be very easy to make.
![[Pasted image 20210926141454.png|350]]
||Resistance||Current||Voltage|
|--|--|--|--|--|--|
|R<sub>1</sub>| | I<sub>R1</sub>| |V<sub>R1</sub>|
|R<sub>2</sub>| | I<sub>R2</sub>| |V<sub>R2</sub>|
|R<sub>3</sub>| | I<sub>R3</sub>| |V<sub>R3</sub>|
|R<sub>12</sub>| | I<sub>R12</sub>| |V<sub>R12</sub>|
|R<sub>23</sub>| | I<sub>R23</sub>| |V<sub>R23</sub>|
|R<sub>T</sub>| | I<sub>T</sub>| |V<sub>T</sub>|
### 1. Use Given Values
From the schematic [[Pasted image 20210926141454.png|➡]], we know the values of each resistor, as well as V<sub>T</sub>:
||Resistance||Current||Voltage|
|--|--|--|--|--|--|
|R<sub>1</sub>|*100Ω* | I<sub>R1</sub>| |V<sub>R1</sub>|
|R<sub>2</sub>| *1KΩ*| I<sub>R2</sub>| |V<sub>R2</sub>|
|R<sub>3</sub>| *4.7KΩ*| I<sub>R3</sub>| |V<sub>R3</sub>|
|R<sub>12</sub>| | I<sub>R12</sub>| |V<sub>R12</sub>|
|R<sub>23</sub>| | I<sub>R23</sub>| |V<sub>R23</sub>|
|R<sub>T</sub>| | I<sub>T</sub>| |V<sub>T</sub>|*9V*|
### 2. Apply Laws and Rules to Solve
These do not necessarily always happen in the same order. Sometimes you have a couple of choices, other times with different given information you may have to do other operations first.
#### Rule: Resistors in Series
Since we have just learned that resistors simply add together in a series circuit, we can now fill in three more squares:
- R<sub>12</sub> = R<sub>1</sub> + R<sub>2</sub> = 100Ω + 1000Ω = 1.1KΩ
- R<sub>23</sub> = R<sub>2</sub> + R<sub>3</sub> = 1000Ω + 4.7KΩ = 5.7KΩ
- R<sub>T</sub> = R<sub>1</sub> + R<sub>2</sub> + R<sub>1</sub> = 100Ω + 1000Ω + 4.7KΩ = 5.8KΩ
||Resistance||Current||Voltage|
|--|--|--|--|--|--|
|R<sub>1</sub>|100Ω | I<sub>R1</sub>| |V<sub>R1</sub>|
|R<sub>2</sub>| 1KΩ| I<sub>R2</sub>| |V<sub>R2</sub>|
|R<sub>3</sub>| 4.7KΩ| I<sub>R3</sub>| |V<sub>R3</sub>|
|R<sub>12</sub>| *1.1KΩ*| I<sub>R12</sub>| |V<sub>R12</sub>|
|R<sub>23</sub>| *5.7KΩ*| I<sub>R23</sub>| |V<sub>R23</sub>|
|R<sub>T</sub>| *5.8KΩ*| I<sub>T</sub>| |V<sub>T</sub>|9V|
#### Ohm's Law
Ohm's law let's us solve for any value if two are known. We now know V<sub>T</sub> and R<sub>T</sub>, so we can use this.
![[Pasted image 20210926125201.png|Ohm's Law]]
We can derive the formula $I = \frac{V}{R}$ and solve for $I_T$:
$\begin{align}
I_T &= \frac{V_T}{R_T}\\
\\
&=\frac{9V}{5.8kΩ} \\
\\
&=0.001552A = 1.6mA
\end{align}$
Note the use of [[T110T SSGW06#Rounding and Estimates|rounding]] to one decimal point, and the use of the proper [[T110T SSGW08#Metric Prefixes|prefix]] rather than the full number with 6 digits to the right of the decimal point. There are no rules as such for this, but notice how a single digit after the decimal is much easier to read. You may default to this unless you require (or are instructed to show) more precision.
||Resistance||Current||Voltage|
|--|--|--|--|--|--|
|R<sub>1</sub>|100Ω | I<sub>R1</sub>| |V<sub>R1</sub>|
|R<sub>2</sub>| 1kΩ| I<sub>R2</sub>| |V<sub>R2</sub>|
|R<sub>3</sub>| 4.7kΩ| I<sub>R3</sub>| |V<sub>R3</sub>|
|R<sub>12</sub>| 1.1kΩ| I<sub>R12</sub>| |V<sub>R12</sub>|
|R<sub>23</sub>| 5.7kΩ| I<sub>R23</sub>| |V<sub>R23</sub>|
|R<sub>T</sub>| 5.8kΩ| I<sub>T</sub>| *1.6mA*|V<sub>T</sub>|9V|
#### Kirchoff's Law for Current
We have just learned [[T105 Week 4#Kirchoff's Law of Current|Kirchoff's Law of Current]], and so we have 5 "free squares" to fill in. These are officially calculations, but really...
In all seriousness though, note how much you know about this circuit. Every square is a piece that you now know about this circuit. You were promised that by the end of the course, you would build a circuit and know every last parameter anywhere in the circuit. Here is where we start putting it together. [[Pasted image 20220815083230.png|😎]]
||Resistance||Current||Voltage|
|--|--|--|--|--|--|
|R<sub>1</sub>|100Ω | I<sub>R1</sub>| *1.6mA*|V<sub>R1</sub>|
|R<sub>2</sub>| 1kΩ| I<sub>R2</sub>| *1.6mA*|V<sub>R2</sub>|
|R<sub>3</sub>| 4.7kΩ| I<sub>R3</sub>| *1.6mA*|V<sub>R3</sub>|
|R<sub>12</sub>| 1.1kΩ| I<sub>R12</sub>| *1.6mA*|V<sub>R12</sub>|
|R<sub>23</sub>| 5.7kΩ| I<sub>R23</sub>| *1.6mA*|V<sub>R23</sub>|
|R<sub>T</sub>| 5.8kΩ| I<sub>T</sub>| 1.6mA|V<sub>T</sub>|9V|
#### Ohm's Law
Again, you will see these applied in different order, depending on the situation. Here we see opportunities to apply Ohm's Law to continue solving.
V<sub>R1</sub> = R<sub>1</sub> x I<sub>R1</sub> = 1.6mA x 100Ω = Did you try this one in your head first? 160mV
We can also solve for V<sub>R2</sub> and V<sub>R3</sub>
||Resistance||Current||Voltage|
|--|--|--|--|--|--|
|R<sub>1</sub>|100Ω | I<sub>R1</sub>| 1.6mA|V<sub>R1</sub>|*160mV*
|R<sub>2</sub>| 1kΩ| I<sub>R2</sub>| 1.6mA|V<sub>R2</sub>|*1.6V*
|R<sub>3</sub>| 4.7kΩ| I<sub>R3</sub>| 1.6mA|V<sub>R3</sub>|*7.3V*
|R<sub>12</sub>| 1.1kΩ| I<sub>R12</sub>| 1.6mA|V<sub>R12</sub>|
|R<sub>23</sub>| 5.7kΩ| I<sub>R23</sub>| 1.6mA|V<sub>R23</sub>|
|R<sub>T</sub>| 5.8kΩ| I<sub>T</sub>| 1.6mA|V<sub>T</sub>|9V|
### Choices
We now have two ways to solve for V<sub>R12</sub>. We can either add V<sub>R1</sub> and V<sub>R2</sub>, or we can use Ohm's Law to solve it.
Notice we can do the very same for V<sub>R23</sub>.
And here we have an important step that will ensure that you have done this work correctly. We can use [[T105 Week 4#Kirchoff's Law of Voltage|Kirchoff's Law of Voltage]] to verify that V<sub>T</sub> = V<sub>R1</sub> + V<sub>R2</sub> +V<sub>R3</sub>
||Resistance||Current||Voltage|
|--|--|--|--|--|--|
|R<sub>1</sub>|100Ω | I<sub>R1</sub>| 1.6mA|V<sub>R1</sub>|160mV
|R<sub>2</sub>| 1kΩ| I<sub>R2</sub>| 1.6mA|V<sub>R2</sub>|1.6V
|R<sub>3</sub>| 4.7kΩ| I<sub>R3</sub>| 1.6mA|V<sub>R3</sub>|7.3V
|R<sub>12</sub>| 1.1kΩ| I<sub>R12</sub>| 1.6mA|V<sub>R12</sub>|1.7V
|R<sub>23</sub>| 5.7kΩ| I<sub>R23</sub>| 1.6mA|V<sub>R23</sub>|8.8V
|R<sub>T</sub>| 5.8kΩ| I<sub>T</sub>| 1.6mA|V<sub>T</sub>|9V|
Here's a recap:
![[Pasted image 20210926171925.png|Insert Given Information]]
![[Pasted image 20210926172442.png|Add Resistances]]
![[Pasted image 20210926172546.png|Ohm's Law to Solve for Current]]
![[Pasted image 20210926172644.png|Kirchoff's Law to Solve for Current]]
![[Pasted image 20210926172910.png|Ohm's Law to Solve for Voltage]]
![[Pasted image 20210926173122.png|Add Voltages]]
![[Pasted image 20210926173402.png|Verify by Adding Voltages and Ohm's Law]]
## This week in the Lab
[[T105L W04|This week]] you will build a similar circuit to last week, but now you will calculate all values, and measure all values. It would be good if you could fill out the table before entering the lab, it will give you more time to do your measurements and experiments.
There is the potential for several "a ha" moments in this lab. You should be satisfied that you understand everything that is happening in our circuit before you consider this week's work done.
Now would be a good time to make sure that all that we have looked at so far is clear to you. Everything so far is foundational for what is to follow. You must be ready to proceed, and the only way to do that effectively is to make sure you are very confident of the material so far. If you are not, contact your prof, ask a question in class, or send me an email at
[email protected] or on discord: @Stratocat
# Lab
[[T105L WS04.pdf|Lab Worksheet]] | [[T105L EQ W04|Equipment List]]
Review the [[T105L SAFETY|Safety Briefing]]
## Lab Prep
Do all calculations for the following circuit filling out the [[T105L WS04.pdf|lab worksheet]]. Follow [[T105 Week 4#Calculating Values in a Circuit|this example]].
- Use correct units for all entries
- Ω, A, V
- Includes using proper [[T110T SSGW08#Metric Prefixes|prefix]], e.g. 1.5mA rather than .015A
- Round to 1 decimal place where applicable
![[Pasted image 20210928070744.png|Series Circuit 1]]
%%
||ResΩ|Meas||Amps|Meas||Volts|Meas|
|--|--|--|--|--|--|--|--|--|
|R<sub>1</sub>|| | I<sub>R1</sub>|| |V<sub>R1</sub>||
|R<sub>2</sub>|| | I<sub>R2</sub>|| |V<sub>R2</sub>||
|R<sub>3</sub>|| | I<sub>R3</sub>|| |V<sub>R3</sub>||
|R<sub>12</sub>|| | I<sub>R12</sub>|| |V<sub>R12</sub>||
|R<sub>23</sub>|| | I<sub>R23</sub>|| |V<sub>R23</sub>||
|R<sub>T</sub>|| | I<sub>T</sub>|| |V<sub>T</sub>||%%
---
## In the lab:
We will be measuring current this week to round out the main types of measurements that can be taken with a multimeter. To accomplish this, you will need to become familiarized with the ammeter function of a digital multimeter.
### Ammeter
You can refer to the [[Bench DMM.pdf|User's Guide]] for full details.
To use the benchtop multimeter, you will need to both turn on power to the workbench and the multimeter itself:
If the main power switch is in the on position but not glowing, check that the circuit breaker to the left of it is not tripped and reset the circuit breaker as necessary or ask an instructor for assistance.
Press the DCI button to put the multimeter in DC Ammeter mode:
You will need to connect test leads or cables to the multimeter through which it will interact with your electrical circuit. Plug the ends of your cables to the colour-coded sockets marked in the diagram below:
Because the whole point of a multimeter is to be a versatile yet accurate measuring instrument, it has the capability to display its measured current at different ranges.
Ranging is normally taken care of automatically by the multimeter, but you can manually set it to operate at various different current ranges by pressing the up and down arrow buttons depicted below. You can revert back to Auto Range by first pressing the blue Shift button, followed by pressing the up arrow button. Note that this should already be familiar to you from using the voltmeter and ohmmeter functions of the DMM.
>STOP
Read the following slowly:
>You must measure current in series with the circuit
- To measure the current, we must be in the path of current flow
- If we insert leads such that we create a short circuit with the power supply, there will be no current limiting (no resistors because we shortcutted them) and overcurrent will result. Because this is an easy enough mistake to make, the multimeter circuitry is protected with a fuse, changeable in the rear of the instrument.
- To adopt to the realities of our training aid in the lab, we will remove a length of wire and replace it with the ammeter to achieve series measurement.
Watch this video [[V Measuring Current|🎞]]
## 1. Build Circuit 1
Basically the same circuit we saw last week, but this time with wires between resistors for measuring current. Supply voltage from the power supply is 9VDC, 300mA.
Complete the lab worksheet by:
### Measuring resistance:
Remember how we isolated a resistor from the circuit in [[T105L W03#d|last week's lab]].
>❗Do not apply power when measuring resistance.
### Measuring voltage:
Apply power and measure voltages for all applicable blanks in the table for circuit 1.
### Measuring current:
Following [[T105L W04#Ammeter|this tutorial]], measure current as required to fill in the table.
>You must measure current in series. Your meter is in the single path for current. If you do not understand, call the prof over before continuing.
## Build Circuit 2
We will now simply exchange two resistors and examine the effects on the circuit. You will need to perform all calculations again.
>Or will you?
Apply your electrical knowledge before you proceed. Has the total resistance changed? Has the total current? What exactly has changed by swapping R<sub>1</sub> and R<sub>2</sub>?
### ALL measurements
Carry out all measurements to complete the table in your lab worksheet.
What did you observe as a result of changing the two resistors? What changed? What did not change? What effect did this change have at the voltage read at V<sub>23</sub>?
## Measure across an open
You will cause an open in the circuit by removing one of the lengths of wire, as if you were going to measure current:
You will apply power, and measure the voltage across the open. Did you get the reading you expected?
Open the circuit at another place. Measure the voltage. Did you get the reading you expected?
See if you can apply what you have learned to solve this common misunderstanding.
You could try to fill out the table again, but based on the circuit being open. Then we would ask the following questions:
- How much current is flowing through the resistors?
- If no current is flowing, how much voltage is dropped over the resistors?
- If the resistors are not dropping any voltage, how much voltage is still available?
This may not be at all intuitive to you at this point. You may need some time to put all of these pieces together to understand that over an open in a simple series circuit like this, we will measure the full power supply voltage. Not high voltage, not some voltage, ALL of the voltage supplied by the power supply. Since the circuit is open and therefore current is not flowing, the potential, or voltage, remains untapped.
Now, do yourself a favour and put the circuit back together and measure the voltage over a length of wire.
And then keep this in your head:
>V over a short = 0
V over an open = MAX
Once we learn about parallel circuits and how resistance behaves there, we will return to this concept and explain it with additional knowledge about the meter circuitry. For now, we can explain this concept using the laws of electricity.
%%
## 2
Same circuit, switch R1 and R2
