Fall2023 Simple Electrical Circuits Lab Online-2
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University of Texas, San Antonio *
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1631
Subject
Electrical Engineering
Date
Apr 3, 2024
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Uploaded by DrToad4406
Simple Electrical Circuits Lab Online
Purpose
The purpose of this activity is to examine how Ohm’s Law can be applied to simple resistors arranged in simple electrical circuits.
Theory
Ohm’s Law tells us that resistance of an object is proportional to the voltage applied to it, and inversely proportional to the induced current passing through it.
R
=
∆V
i
When multiple resistors are arranged in
series
and a steady stream direct current is flowing through them we have three rules related to the current, the voltage, and the resistance of all of those resistors together. Those three rules are as follows:
1.
For resistors in series the current passing through each of them is the same.
i
=
i
j
=
i
1
,i
2
,i
3
…
2.
For resistors in series the voltage being applied to all of them is the sum of the voltage passing over all of them
∆V
=
∑
j
n
∆V
j
=
∆V
1
+
∆V
2
+
∆V
3
+
…
3.
For resistors in series the equivalent resistance of all of them together is just the sum of all of their resistance.
R
eq
=
∑
j
n
R
j
=
R
1
+
R
2
+
R
3
+
…
1
When multiple resistors are arranged in
parallel
and a steady stream direct current is flowing through them we have three rules related to the current, the voltage, and the resistance of all of those resistors together. Those three rules are as follows:
1.
For resistors in parallel the total current passing through all of them is the sum of the current passing through each of them.
i
=
∑
j
n
i
j
=
i
1
+
i
2
+
i
3
+
…
2.
For resistors in parallel the voltage passing over each of them is the same.
∆V
=
∆V
j
=
∆V
1
,∆V
2
,∆V
3
,…
3.
For resistors in parallel the inverse of the equivalent resistance of all of them is the sum of the inverses of all of them.
1
R
eq
=
∑
j
n
1
R
j
=
1
R
1
+
1
R
2
+
1
R
3
+
…
When using these two sets of equations it can be best to draw simple circuit diagrams to help determine which circuit components are in series with each other, and which are parallel to each other. Let us start by examining two basic circuit component symbols.
1.
A Potential Difference Source - Power supply, battery, fuel cell, or anything that will induce a potential difference to exist in the circuit. The circuit diagram symbol for such a
device is two uneven parallel lines. The longer line represents the positive side of the Voltage Source, and the shorter line its negative side. The lines pointing out of both sides represent the wires that will connect the Voltage Source to the rest of the circuit.
2.
Resistors – A component that hinders the flow of current through the circuit. Resistors are represented by few sharp jagged lines right in row.
2
This is drawn with the connecting wires coming out of both ends.
Setup Part 1: Resistors in Series 1.
Go to the following website:
https://phet.colorado.edu/en/simulation/circuit-construction-kit-dc-virtual-lab
2.
You should now see the following:
3.
Click the down arrow to download the software. Once finished, you should see the following:
4.
Near the bottom left of the screen, click on the Potential Difference symbol.
3
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5.
On the right side of the screen just below the Voltmeter & Ammeter, click the Green/White Plus symbol next to Advanced.
6.
In the drop-down menu for Advanced, make sure that Wire Resistivity and Battery Resistance are both set to ‘tiny’, then click the Red/Minus to close the drop-down menu. 7.
In the White Box at the top right of your screen make sure “Show Current” is checked, select “Conventional”, make sure “Labels” is checked, and make sure that “Values” is checked.
Procedure Part 1
1.
On the Left side of your screen you will see a white box with the symbols of various basic circuit components. You will ‘Click and Drag” the various components to build simple circuit boards. 2.
On the right side of your screen, and about a third of the way from the top you will see a white box with a voltmeter and an ammeter. You will ‘insert’ these instruments into the circuit you build in order to measure the voltage and the current. 3.
Build the following circuit of three resistors in series with each other: (You can use the plus and minus at the bottom of the left side of your screen to give yourself more room to work with if you need it.)
4.
Click on the Potential Difference source (Battery) and set it to 100 V.
5.
Click on each of the resistors to set its resistance. Set R
1
= 10.0 Ohms, R
2 = 50.0 Ohms, and R
3 = 100.0 Ohms. 6.
Read off the currents for each ammeter in front of each resistor and record the currents for each resistor in Table 1.
7.
Using the voltage meter, measure the voltage for each resistor and record those voltages in Table 1.
a.
Remember that the voltmeter probes have to go on opposite ends of the resistor to get a reading.
4
b.
If you get a negative voltage just record the absolute value. [This just means you put the positive probe (red) at the negative end of the resistor, and the negative probe (black) at the positive end of the resistor.] Setup Part 2: Resistors in Parallel 1.
Use the orange button in the bottom right of your screen to reset the simulator.
a.
Your screen should now look like the following:
2.
Near the bottom left of the screen, click on the Potential Difference symbol.
3.
On the right side of the screen just below the Voltmeter & Ammeter, click the Green/Plus symbol next to Advanced.
4.
In the drop-down menu for Advanced, make sure that Wire Resistivity and Battery Resistance are both set to ‘tiny’, then click the Red/Minus to close the drop-down menu. 5.
In the White Box at the top right of your screen make sure “Show Current” is checked, select “Conventional”, make sure “Labels” is checked, and make sure that “Values” is checked.
Procedure Part 2: Resistors in parallel
1.
Build the following circuit of three resistors in parallel with each other: (You can use the plus and
minus at the bottom of the left side of your screen to give yourself more room to work with if you need it.)
5
2.
Set the Potential Difference (Battery) to 50.0 V, and the resistors as follows, R
1
= 10 Ohms, R
2
= 50.0 Ohms, and R
3
= 100.0 Ohms. 3.
Record the currents for each resistor in Table 2. Using the voltmeter, measure the voltage for each resistor, and then record your measurements in Table 2.
Setup Part 3: Resistors in a mix of series and parallel
1.
Use the orange button in the bottom right of your screen to rest the simulator.
a.
Your screen should now look like the following:
2.
Near the bottom left of the screen, click on the Potential Difference symbol.
6
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3.
On the right side of the screen just below the Voltmeter & Ammeter, click the Green/Plus symbol next to Advanced.
4.
In the drop-down menu for Advanced, make sure that Wire Resistivity and Battery Resistance are both set to ‘tiny’, then click the Red/Minus to close the drop-down menu. 5.
In the White Box at the top right of your screen make sure “Show Current” is checked, select “Conventional”, make sure “Labels” is checked, and make sure that “Values” is checked.
Procedure Part 3: Resistors in a Mix of Series and Parallel
6.
Build the following circuit: (You can use the plus and minus at the bottom of the left side
of your screen to give yourself more room to work with if you need it.)
7.
Set the Potential Difference (Battery) to 50.0 V, and the resistors as follows, R
1
= 10 Ohms, R
2
= 25.0 Ohms, R
3
= 40.0 Ohms, and R
4
= 100.0 Ohms. 8.
Record the currents for each resistor in Table 3. Using the voltmeter, measure the voltage for each resistor, and then record your measurements in Table 3.
7
Analysis of Simple Electrical Circuits
Lab Online
Name: Wyatt Collier Course/Section: PHY-1631-007
Instructor: Dale Bobar
For each of the three simple circuit boards you will need to calculate the total resistance, R
eq
, for the entire circuit board by using the measured resistances of each of the resistors, and the equations given to you in the theory section. Use the applied voltage for each setup as the theoretical voltage, V
th
, for the entire circuit board, to calculate the theoretical current, i
th
, for the entire circuit board. Table 1(Resistors in Series) R(Ω)
i
ex
(A)
V
ex
(V)
i
th
(A)
V
th
(V)
% Error i
% Error V
R
eq
160
0.62
100
0.625
100
0.8
10Ω
10
0.62
6.25
0.625
6.25
0.8
0
50Ω
50
0.62
31.25
0.625
31.25
0.8
0
100Ω
100
0.62
62.50
0.625
62.50
0.8
0
1.
Using the equations for resistors in series calculate the theoretical voltages, and currents for each of the resistors, and the entire circuit. Use the measured values of the resistance in your calculations. Then calculate the % errors. Show work. (20 points)
R
eq
=
10
+
50
+
100
=
160
Ω
I
=
I
1
, I
2
, I
3
=
0.62
ΔV
=
V
1
+
V
2
+
V
3
=
6.25
+
31.25
+
62.50
=
100
V
|
0.625
−
0.62
|
0.62
∗
100
=
0.8%
|
6.25
−
6
.
25
|
6
.
25
∗
100
=
0%
|
31.25
−
31.25
|
31.25
∗
100
=
0%
|
62
.
50
−
62
.
50
|
62
.
50
∗
100
=
0%
2.
According to our equations, what should be the relationship between the total current and the currents passing through each resistor? Does your data show this relationship? (5 points)
8
The relationship between the total current and the currents passing through each resistor is that both should be equivalent in a series. The data from the table reflects this.
3.
According to our equations, what should be the relationship between the total voltage and the voltages passing over each resistor? Does your data show this relationship?
(5 points)
The relationship between the total relationship and the voltages passing over each resistor is that as the resistor gets larger, the voltage passing through each resistor gets larger as well. This can be represented by the summation of all three voltages, given by the equation V
=
V
1
+
V
2
+
V
3
. The data shows this relationship. Table 2(Resistors in Parallel)
R(Ω)
i
ex
(A)
V
ex
(V)
i
th
(A)
V
th
(V)
% Error i
% Error V
R
eq
7.7
6.50
50
6.50
50
0
10Ω
10
5.00
50
5.00
50
0
0
50Ω
50
1.00
50
1.00
50
0
0
100Ω
100
0.50
50
0.50
50
0
0
4.
Using the equations for resistors in parallel calculate the theoretical voltages, and currents for each of the resistors, and the entire circuit. Use the measured values of the resistance in your calculations. Then calculate the % errors. Show work (20 points)
R
eq
=
(
(
1
R
1
)
+
(
1
R
2
)
+
(
1
R
3
)
)
−
1
=
(
(
1
10
)
+
(
1
50
)
+
(
1
100
)
)
−
1
=
7.7
Ω
i
ex
(
A
)
=
I
1
+
I
2
+
I
3
=
5.00
+
1.00
+
0.50
=
6.50
A
i
th
(
A
)
=
I
1
+
I
2
+
I
3
=
5.00
+
1.00
+
0.50
=
6.50
A
(
50
10
)
=
5.00
A
(
50
50
)
=
1.00
A
(
50
100
)
=
0.50
A
|
6.5
−
6.5
|
6.5
∗
100
=
0%
|
5.00
−
5.00
|
5.00
∗
100
=
0 %
|
1.00
−
1.00
|
1.00
∗
100
=
0%
|
0.5
−
0.5
|
0.5
∗
100
=
0%
9
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|
50
−
50
|
50
∗
100
=
0%
5.
According to our equations what should be the relationship between the total current and the currents passing through each resistor? Does your data show this relationship? (10 points)
The relationship between the total current and the currents passing through each resistor is given equal to the summation of all resistors, given by the equation: I
=
I
1
+
I
2
+
I
3
. The data reflects this relationship.
6.
According to our equations what should be the relationship between the total voltage and the voltages passing over each resistor? Does your data show this relationship? (10 points)
The relationship between the total voltage and the voltages passing over each resistor is
V
=
V
1
+
V
2
+
V
3
, where each voltage is the same amount. This relationship is displayed in the data collected.
Table 3(Resistors in both Series and Parallel) R(Ω)
i
ex
(A)
V
ex
(V)
i
th
(A)
V
th
(V)
% Error i
% Error V
R
eq
63.57
0.79
50
0.79
50
0
10Ω
10
0.79
7.87
0.79
7.90
0
0.003
25Ω
25
0.79
19.66
0.79
19.75
0
0.005
40Ω
40
0.56
22.47
0.56
22.35
0
0.005
100Ω
100
0.22
22.47
0.2235
22.35
0.02
0.005
7.
Using the equations for resistors in series and in parallel, calculate the theoretical voltages and currents for each of the resistors, and the entire circuit. Use the measured values of resistance in your calculations, then calculate the % errors. Show work. (20 points)
R
eq
=
R
1
+
R
2
+
(
(
1
R
3
)
+
(
1
R
4
)
)
−
1
=
10
+
25
+
(
(
1
40
)
+
(
1
100
)
)
−
1
=
63.57
Ω
I
=
(
V
R
eq
)
=
(
50
63.57
)
=
0.79
A
V
1
=
I
1
R
1
=
(
0.79
) (
10
)
=
7.90
V
V
2
=
I
2
R
2
=
(
0.79
) (
25
)
=
7.90
V
10
V
3
=
V
4
=(
50
−
19.75
−
7.90
)=
22.35
V
I
3
=
(
V
3
R
3
)
=
(
22.35
40
)
=
0.56
I
4
=
(
V
4
R
4
)
=
(
22.35
100
)
=
0.56
|
0.79
−
0.79
|
0.79
∗
100
=
0%
|
0.2235
−
0.2235
|
0.2235
∗
100
=
0%
|
7.90
−
7.87
|
7.90
∗
100
=
0.003%
|
19.75
−
19.66
|
19.75
∗
100
=
0.005%
|
22.47
−
22.35
|
2.35
∗
100
=
0.005%
8.
Do the results of the experiment agree with theoretical predictions for resistors in series and parallel?
Explain your answer. (10 points)
Yes, the results of the experiment agree with theoretical predictions for resistors in series and in parallel. The experimental values and the theoretical values were like each other, and the percent error between them was close to 0%. Therefore, the results agree with the theoretical predictions
11
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