Lab Report 2: For Good Measure: Basic Circuits

Eli Barrow & Isaac Stevens
Jan. 25, 2024

Summary of Lab

There were multiple goals of this lab, the most important goals were to learn how to solder and analyze circuits to further understand KVL and KCL. The work performed in this lab was very intriguing and it allowed us to stay focused on the bigger picture of the lab and what we were trying to accomplish. The soldering was a fun addition to the lab where we got to do some hands-on building rather than just aimlessly taking different measurements. At the end of the lab, it was easily seen that our group benefited greatly from the material presented, mostly because all of the topics we had only worked with conceptually and not had any hands-on experience with.

Lab Schematics and Procedure

For Lab 2, the following materials are required:

• A Digital Multimeter

• A DC Power supply

• A Soldering station

• A small piece of solder

• Resistors: 1kΩ, 2.2 kΩ, 5.1 kΩ, 4.7 kΩ, 6.8 kΩ, 15 kΩ, 220 kΩ

• Soldering Breadboard (In our case, a DigiKey SolderFul BreadBoard)

• Regular Breadboard

Part 1 - Series Circuit

Begin by turning on the soldering station to 400 °C and give it time to reach the designated temperature. Make sure the tip is in proper condition and if not either replace the tip or tin the tip if necessary.

Below is a picture of the soldering station our group used in class.

Grab the soldering breadboard and create the following circuit with the resistors in the same order as shown. Before using the resistors, verify the resistance with the DMM.

After creating the circuit on the breadboard, grab the soldering iron and apply the solder to the meeting point between the resistors and the copper pad. Make sure to apply and feed the solder to the soldering iron to effectively solder the resistor to the breadboard.

If done properly, the back of the breadboard should look like this:

Next, connect the DC Power Supply and set the voltage to 10V and the current to 0.250A. The complete circuit should look something like the image below.

Then, setup the DMM as shown in the picture below to measure the voltage drop across $R_1$ (1 kΩ), $R_2$ (2.2 kΩ), and $R_3$ (5.1 kΩ) and record the results.

Move the DMM to be in series with the circuit so the current can be measured. Since the circuit is in a series there will be only one current. Record the current.

Our group moved the DMM to be in series by doing as shown in the picture below.

Part 2 - Parallel Circuit

Build the following parallel circuit on the normal breadboard using the schematic below. Make sure the resistors are in the same order as shown and before using the resistors, verify the resistance with the DMM.

Next, connect the DC Power Supply and set the voltage to 10V and the current to 0.250A. The complete circuit should look something like the image below.

Use the DMM in parallel with the $R_5$ (2.2 kΩ) to measure the voltage drop across $R_5$. Next, use the DMM in series with R5 to measure the current across the resistor.

Next, follow the schematic below and remove R5 from the circuit.

Next, measure and record the current of $I_1$ ($R_1$=4.7 kΩ), $I_2$ ($R_2$=6.8 kΩ), and $I_3$ ($R_4$=220 kΩ) by putting the DMM in series with the corresponding resistors as shown below.

Keep $R_5$ disconnected from the circuit and setup the DMM in parallel with resistors to measure the voltage drop across $R_1$ (4.7 kΩ), $R_2$ (6.8 kΩ), $R_3$ (15 kΩ), and $R_4$ (220 kΩ). Record the results.

Finally, answer the discussion questions associated with the lab.

No code is required to replicate the lab.

Lab Assignment Specific Items

Objective 1: Learn soldering techniques by building a simple circuit on a solder breadboard

Part 1 - Series Circuit

In this step of the lab we practiced our soldering skills and soldered together the circuit shown above. This was a very useful skill to learn in the lab and was a simple ciruit to solder for our first time.

Objective 2: Analyze a circuit to verify Kirchhoff’s voltage law (KVL) and Kirchhoff’s current law (KCL), and to apply Thevenin’s and superposition theorems to the analysis of electrical circuits.

Part 1 - Series Circuit

Using the DMM we measured the voltage drop across each resistor along with the current that is present in the circuit. The results are shown in the table below.

Type	Measured
Voltage Drop	$R_1$ = 1.2V
Voltage Drop	$R_2$ = 2.675V
Voltage Drop	$R_3$= 6.125V
Current	I = 1.21mA

Part 2 - Parallel Circuit

Using the DMM we measured the voltage ($V_L$) drop across $R_5$ and measured the current ($I_L$) through $R_5$. The results are shown in the table below

	Measured
$V_L$ (Voltage acrros $R_L$ / $R_5$)	3.565 V
$I_L$ (Current through $R_L$ / $R_5$)	1.64 mA

Using the DMM we measured the currents $I_1$, $I_2$, $I_3$ without $R_5$ in the circuit.

Current	Measured	Calculated
$I_1$ (For $R_1$)	-0.50 mA	2.55 mA
$I_2$ (For $R_2$)	0.46 mA	0.55 mA
$I_3$ (For $R_4$)	0.04 mA	0.055 mA
Note:

Here we can easily see that our measured values from the DMM do not match up to our calculated values, therefore we made some sort of error in our calculations not giving us the correct calculated values.

Part 2.2 - KVL

This step begins with $R_5$ still removed from the circuit.
Using the DMM we measured the voltage drop across all the resistors.

Voltage	Measured Mag.	Calculated Voltages
$V_1$	2.292 V	11.985 V
$V_2$	3.026 V	3.74 V
$V_3$	6.686 V	8.25 V
$V_4$ (same as $V_5$)	9.70 V	12.1 V

Note: Here we can easily see that our measured values from the DMM do not match up to our calculated values, therefore we made some sort of error in our calculations not giving us the correct calculated values.

Discussion Question 1: How much power does each resistor dissipate? Each branch? Total power? Is the power in equal to the power out? Using the equation P=IV with P=power, I=Current, and V=Voltage, we find $P_1$=-1.146 mW, $P_2$=1.392 mW, $P_3$=3.08 mW, and $P_4$=0.388 mW. For branches, Branch $P_1$=-1.146 mW, Branch $P_2$=4.472 mW, and Branch $P_3$=0.388 mW. $P_T$=3.714 mW and $P_I$ < $P_O$.

Part 2.3 - Thevenin

Thevenin’s Theorem states that all linear circuits, regardless of the number of components, can be expressed as a circuit with one equivalent voltage source and one equivalent resistance.

The original circuit that we were given is shown below:

The first step in the Thevenin process is to remove the load in the circuit. In this case, the load was $R_5$. The updated circuit is shown below:

We then simplified the circuit to increase the ease of calculating our values $R_T$, $V_T$, $I_N$, $V_L$, and $I_L$. The updated circuit is shown below:

We then calculated $R_T$, $V_T$, $I_N$, $V_L$ and $I_L$ using the previously measured values for $R_1$, $R_2$, $R_3$, and $R_4$. Using nodal analysis we were able to calculate $V_T$.

	Calculated
$R_T $	3.800 kΩ
$V_T$	9.701 V
$I_N$	2.553 mA
$I_L$	1.617 mA
$V_L$	6.145 V

Discussion Question 2: Does $I_T$ = $I_L$?

In this circuit that we were given the way that $I_T$ would be calculated would be to insert the load resistor back into the circuit, and then calculate the current running through the load by using Ohm's law using the Thevenin voltage and load resistor value. This would give you the Thevenin current, in the lab questions we were asked to calculate $I_L$ as well, and the previous steps listed above are what procedure was followed to get the value for $I_L$. So the answer to this discussion question is YES, $I_T$ = $I_L$.

Outcome and Conclusion

The lab's outcome was that voltage and current could be measured and calculated in a series circuit and a parallel circuit. The calculations for voltage and current were able to be completed through KVL and KCL laws. Thevenin Theorems were also applied to calculate $V_L$ and $I_L$ for the parallel circuit. The last outcome of the lab was a circuit was soldered successfully and used as the series circuit in the lab. This lab concluded that KVL, KCL, and Thevenin laws can be applied to either a parallel or series circuit to analyze circuits properly. If these laws are applied properly elements within the circuit can become known and be used to predict and explain values in real-world circuits. However, due to our group's inexperience, some of the calculations in the lab may not be correct compared to their real-world measurements which were taken with the DMM. Another conclusion from this lab is soldering components to a solder breadboard is a viable method to create more structurally sound circuits in the real world.