Thevenin Equivalents

Objectives:

1. Figure out the thevenin Resistance in a given circuit by:
a. finding the open circuit voltage
b. finding the short circuit current
c. applying Rth = Voc / Isc
2. Determine the smallest Resistance for a 8V voltage drop across RL2
3. Test and compare the Thevenin Circuit to the original circuit
4. Verify that the max power across RL2 occurs when RL2 = Rth

Circuit Plan

Objective 1

a. Open Circuit Voltage

b/c. Short circuit current and finding Rth

Objective 2

Finding resistance RL2

Objective 3

Data

Thevenin Equivalent circuit

Component measurements

Experiment

 Note: the percent errors are outstanding which i was hoping for because the nominal values were very close to the measured values of our components.

Now for the

Original Circuit

set up

data

Component measurements

Experiment

Note: again the percent errors are low. And even better, we get about the same measurements that were obtained in the thevenin equivalent circuit.

Objective 4

The picture above also shows the power when RL2 =  Rth

By using a variable resistor box for RL2 we were able to easily to change the resistance for the following tests to measure the voltage across RL2 and in turn calculate the power

Measurement/Calculations

The calculations show that the power is the greater when RL2 = Rth 

Conclusion:

The thevenin equivalent circuit was in fact equivalent to the original circuit. The experiment showed that the voltage across the Load was the same when it had a 824 ohm resistance as well as an infinite resistance.

Extra Credit

SELF-E!

I was there here is the proof:

Transistor Switching

Objectives

1. Familiarize ourselves with transistors by building a simple circuit that uses a transistor a switch and LED.
2. Find the Beta value for the 2N3904 transistor by setting up the circuit shown in the lab manual and graphing the current measurements.

Objective 1:

Values/items used in Diagram:

S1: switch

R1: 180 Ohm resistor

R2: 10 K Ohm resistor

R3: 680 Ohm resistor

Q1: 2N3904 transistor

D1: LED

Circuit Set Up/Diagram

Set up

Conclusion: the LED lights up when the make shift switch is connected, we have done something right.

Objective 2

Circuit set up:

When everything was set up we measured the current between the 10 K potentiometer and the base of the transistor as well as the current leaving the transistor.

Data Points

Using the measured values from the experiment we can graph the two currents to find our Beta value.

mA passing through A1		mA passing through A2
0.11		16.62
0.15		16.7
0.2		16.81
0.25		16.95
0.3		17.07
0.35		17.18
0.4		17.32

Excel graph of data points

By apply a best fit for our data we can conclude that the beta value for the 2N3904 transistor is approximately 2.43. The slope of the line is the Beta value we seek.

Conclusion:

This experiment demonstrates how transistors can be used to either switch the flow of the current or create a gain in current.

Nodal Analysis

Objective: we wish to make a circuit that can still power two loads while obtaining damage from the dangerous world around us.

Circuit Chosen:

Note: this circuit contains multiple batteries which helps to satisfy our objective of damage proofing our circuit. If one battery fails we have one more.

Step 1A: Nodal Equations

Boring Math: (Unless you are into that kind of thing)

Step 1B: VB=V2, VC=V3

Currents:

Note the currents above are shown to be negative due to the orientation given to them in the diagram; however, they would be taken to be positive leaving the battery. 

Show me the POWER: of each battery

Step 3: Chart of nomial and measured values as well as power ratings of each component in circuit.

Note the measured values reasonably resemble the nominal values which would imply lower margins of error when doing final calculations.

Step 5: lets do it

Actual Circuit

Data

Conclusion: the margins of error are larger then i would have expected. If time was unlimited i would have liked to redo the experiment to make sure the circuit was built correctly or other errors were not made. 

Step 6:

Pbat1 = (10.71V)(13.4mA) = 0.144W

Pbat2 = (2.4mA)(10.9V) = 0.0242W

Now we are V2=V3=9V

Circuit Produced:

Measurements

 V2 = 9.05 V

V3 = 9.07 V

Ibat1 = 9.1 mA

Ibat2 = 8.9 mA

Conclusion: the two voltage readings are very close to 9 V makings me feel that we did something right.

The End

Engineering44B.Ellison

Introduction to Biasing

The goal in this lab was to create a circuit that would allow for the functioning of two LEDs with different Voltage and Current ratings. To accomplish this we put the two LEDs in parallel and a resister in series with each LED. Shown bellow is the set up to the circuit.

The requirements for the Red LED was 5V and 22.75mA while the Green LED was rated for 2V and 20mA

Given this information we can use V=iR to find the resistance of the LEDs

R_ledred = 219.8 ohms R_ledgreed =  100 ohms

I_R1 = 22.75mA

I_R2 = 20mA 

Since they are in series with LEDs they will share the same current

V_R1 = 4V

V_R2 = 7V

Since the two series of resisters and LEDs are in parallel the voltage must be 9V. Since we know the voltage we want to obtain across our LEDs we can simply Subtract 9V-2V and 9V-5V

R_1 = 175.8 ohms    R_2 = 350 ohms

P_R1 = 0.091W     P_R2 = 0.14W

Assuming that we are only using cheap commercially offered resistors we will be using R_1 to be 220 Ohms and R_2 to be 470 Ohms.

Circuit set up

Data 

The above is a list of currents and voltages across the LEDs and also shows what happens to the current and voltage when one of the two LEDs is removed.

Additional Questions:

If the 9V battery had and useful life 0.2 A-hr then the circuit would operate for 0.2A-hr/28.04mA = 7.13Hours

(14.78-22.75)/22.75*100 = 35.0 percent error across the RED LED

 and 26.3 percent error across the Green resistor

Most of the error can be attributed to the Resisters since we used resisters that were cheaply available.

Bonus:

If either LED were to be removed then the Voltage and current across the remaining LED would be higher then its rated for, which will cause the LED to burn out.