Superposition 2 Lab

Objective:
We are introduced to Every circuit which helps analyze and simulate a circuit. This chrome application is helpful to understand the values at each resistor or other unknown currents and voltages. We are also introduced to a new method called linearity which its output is linearly related or directly proportional to its input. In other words, the linearity property says that when the cause changes to some amount, the effect changes to the same amount. Finally we deal with superposition and transformation which are methods that make circuit analysis easier to calculate in terms of what we are finding.

Group Practice:
1. The image below shows voltage and current independent source on each side of the circuit and are told to find the current flow through the 5 ohm resistor. In order to accomplish this, we use superposition which is method that enables the current source to be set to zero or voltage to zero. However, it must be done once at a time at each side. Then we acquire the currents and them together as seen in Figure 1.

Figure 1. Superposition class work

Superposition Lab Procedures and Results:

1. In this lab, we must first find theoretical value of voltage by using superposition as seen in figure 2. First we set the voltage source of 3V to zero and find the voltage V1 = 2.2V using current division. Then we set the voltage to the right to zero and find the voltage V2=.71V from that source. Finally we add the voltages V = V1+ V2 from both independent sources. We get a theoretical value of V = 2.9V which seem to be too high but will compare to our experimental value of voltage at 6.8k resistors.

Figure 2. Finding the theoretical voltage at the 6.8k resistor

2. We commence to build our circuit based on the schematic in Figure 3. We notice that we don not have a 20 kilo ohm resistor available in class and change it to a 22k resistor since it is what we have in class and because this value was used to find our theoretical Voltage at the 6.8 resistor.

Figure 3. Schematic for a circuit with two independent voltage sources. 

3. We record the actual resistance of the resistors: R10K = R4.7K = R6.8K = R22K = R1K =

4 . We measure the voltage across the 6.8k resistor while the 3V source is replaced with a short circuit and measure a value of V1 = .69V +/-.01

Figure 4. Value of voltage for V1

5. We measure the voltage across the 6.8k resistor while the 5V sources is replaced with a short circuit and measure a value of V2 = 1.98V +/-.01

Figure 5. Value of voltage of V2

6. We then measure the voltage at the 6.8k resistor with both voltage sources in place and find a value of V = 2.69V +/-.01

Figure 6. Total voltage at the 6.8k resistor

Figure 7. Values for V1 and V2

Summary of Superposition Lab and Learning Outcome:

The theoretical values for voltages V1 and V2 while each of the independent voltages sources are equal to zero correlate and match with our experimental values. We see that their is a low percentage of error for V1 % error = |(2.2-1.98)|/2.2 *100= 10% and V % error = |.71-.69|/.71*100 = 2.8%. Their true Voltage error at the 6.8k resistor is % error = |(2.9-2.69)|/2.9*100 = 7.24%. We can agree that superposition is theoretically correct and serves beneficial for reducing complex circuits to simpler circuits. The final tables with results and percentage error may be seen in figure 7 above.