Lab 5 - Thevenin Equivalents

Objective:
To understand and determine the Thevenin Equivalence within a given circuit

Original Circuit Schematic

The schematic above is the circuit that is used for the lab.  The purpose is to determine the Thevenin Voltage and Resistance for the component labeled RL2.

Pre-Lab Calculations:

Before starting the experiment, the values of RTH and VTH are first calculated using the below two schematics.

Given:

RC1 = 100Ω

RC2 = RC3 = 39Ω

RL1 = 680Ω

VS1 = VS2 = 9V

Calculation for node Vx(VTH) needed for RTH

Calculation for RTH 

Thevenin Equivalent Circuit Schematic

Calculation for smallest permissible RL2, Short-circuit current, and Open-circuit voltage

The calculated values:

RTH = 65.96 Ω

VTH = 8.64337 V

RL2 = 820 Ω

ISC = 0.131068 A

VOC = 8.64 V

The Experiment Model:

Thevenin Equivalent Circuit Schematic:

Config:  RL2 = RL2,min

Config: RL2 = ∞ Ω

Component Measurements

Results for Configurations 

The percent error obtained is pretty small meaning that the results can be assumed to be fairly accurate.  This shows that the Thevenin Equivalent Circuit can be used to determine the values of the variable resistor.

Original Circuit Schematic:

Config:  RL2 = RL2,min

Config: RL2 = ∞ Ω

Component Measurements

Results for Configuration

The percent error obtained is fairly small, which allows for the assumption that the data is accurate.  Since the values are similar to the Thevenin Equivalent Circuit, it can be seen that the Thevenin equivalent components are the same as the variable components of the original circuit. 

Maximum Power Effect:

The results show that when RL2 = RTH is when the maximum power is achieved and when RTH is smaller or larger, it does not produce a larger wattage.

Extra Credit: Selfie from CIE presentation

#selfie#engineering44

Lab 4 - Transistor Switching

Objective:
To understand the usage of a transistor within a circuit.

The Circuit with a Switch:

Right Image: Breadboard Schematic
Left Image: Circuit Schematic

Components:

R1 = 180Ω

R2 = 10k Ω

R3 = 680 Ω

D1 = LED

S1 = Switch ( Push button)

Q1 = Motorola 2N3904 Transistor

With this circuit setup, the switch is used to determine if the circuit will work.  This means that if the switch closes the circuit, turned on, the LED will light and it will not light when the switch is open. Below is a video demonstration that the LED brightly lights up when the switch is closed.

Fingertip Switching: 

The circuit is modified to remove the Pushbutton switch and replace it with a fingertip to act as the switch.

Below is video demonstrations of the fingertip switch working properly.

The LED still lights up but the intensity of the LED is lower than the previous circuit.  This is difference is due to the resistance of each individuals skin on his or her fingertip, so the LED differs in intensity for each person.

The concept being illustrated by both lab demonstrations are a transistor amplifies any changes in current that one apply to its base.

The Circuit with a Potentiometer:

The circuit is modified to use a potentiometer in place of the switch.  This is to see how a transistor functions when potentiometer is placed to adjust the voltage of the base of the transistor.  The images below demonstrate the current flowing through the two ammeters that are connected to the potentiometer and the transistor. 

Measured Values of Current through Ammeter 1 and Ammeter 2: 

Graph of Measured Values: 

From the graph, the relationship of the current running through the Ammeter 1  and Ammeter 2 has a somewhat linear relationship.  It can be assumed that as current flow through Ammeter 1 increases, the current in Ammeter 2 also increases.  This is possible due to the usage of the potentiometer controlling the amount of current flowing through the circuit.

Lab 3 - Nodal Analysis

Objective:
The purpose of the lab is to determine the voltage across two nodes(V2 and V3) using nodal analysis and then use those values to find the power supplied to the circuit from both batteries.

Schematic of Circuit

Step 1 (Calculations before building circuit):

The given values:

VBat1 = 12V

VBat2 = 9V

RC1 = 100Ω

RC2 = RC3 = 220Ω

RL1 = RL2 =  1000Ω

These values were used to determine the values of V2 and V3 using nodal analysis, along with the power and current leaving the batteries. The calculation is  shown below:   

Calculation for V2 and V3

Using Nodal Analysis, V2 = 10.26 V and V3 = 8.67V

Calculation for Current and Power leaving each battery

The current leaving each battery: IBat1 = .0174A and IBat2 = .0015A

The power supplied by each battery: PBat1 = .2088W  and PBat2 = .0135W

The Circuit:

The Measured Values:

Actual Power Supplied:

The Changed Circuit:

For this circuit, it is now assumed at V2 = V3 = 9V and need to find the required battery voltages for the circuit.

Using nodal analysis, it is determined that the battery voltages needed are VBat1 = 9.9V and VBat2 = 10.98V

The Circuit model:

The Measured Values:

Conclusion

The experiment showed nodal analysis can be used to determine the approximate values of the actual measurements of voltage and current through a circuit.  This can be concluded due to the percent errors obtained to be very small, with the largest error being less than 5%.  So it can be assumed that nodal analysis is useful to calculate the voltage and current of a circuit.

Lab 2 - Introduction to Biasing / FreeMat Assignment 1

Objective/Intro:

To simultaneously have two LEDs of different voltages and currents light up without burning out the bulbs while being supplied 9V from a battery source. 

Biasing Solution

The figure above is the schematic for the biasing solution to allow for the LEDs to light up.  

To allow for the biasing to work properly, the values of R1 and R2 must be calculated.

Calculation of Voltage and Current for R1 and R2

Values of R1 and R2 & Power consumed by each resistor

The resistor values obtained for the biasing to properly work:

R1 = 175.8 Ω 

R2 = 350 Ω

However, these resistors are unavailable in lab, so the values are rounded up to the closest commercially-available resistor values:

R1 = 220 Ω

R2 = 470 Ω

Model:

Lab Schematic for Biasing Solution

Lab Model of Biasing Circuit

To model the biasing solution, the circuit is connected to a 9V battery supply and the two LEDs are placed in parallel with one another.  There is a resistor that is series with each of the LEDs to properly bias the two LEDs.  

There are three configurations done for the lab:

Configuration 1: Both LEDs in the circuit

Configuration 2: Remove LED2 (RLED2) from the circuit

Configuration 3: Remove LED1 (RLED1) from the circuit

Configuration Data:

Questions/Calculations:

d. With the 6V battery, the efficiency of the circuit will go up.  The "best" efficiency would be obtained by using a battery voltage of 5V.  

The efficiency with the 5V battery:

Pin = 5V * Isupply = 5 * ( 27.82*10^-3) = 0.1391 W

Pout = 0.110927W

Efficiency = Pout/Pin * 100 = (0.110927/0.1391 )*100 = 79.75%

Free Mat Assignment 1

Lab 1: Introduction to DC Circuits

Objective:

The purpose of this lab is to determine the maximum permissible cable resistance required to allow the load to function normally, the maximum distance the battery and load can be separated if an AWG #30 cable is used, the distribution efficiency of the circuit, and the approximate time for the battery to discharge.

The figure above is the original schematic of the experiment.  The figure below is the schematic set-up used to model the original schematic, with RcableTot representing the cables.  

Model:

To model the second schematic in the objective section, a power supply is used to represent the battery, a resistor of known resistance, 1000 Ω, represents the "Load", and a resistor box to represent the unknown resistance of the cables.  An ammeter is set in series with the circuit to measure the total current circulating within the circuit.  The voltmeter is placed in parallel with the "Load", the 1000 Ω resistor, to measure the voltage across it.  

Data:

Known Values:

PLoad = 0.144W when supplied 12V

Capacity rating of battery = 0.8 Ahr

Resistor Box Power Rating = 1 W

Theoretical Value :

RLoad = V^2/P = (12 )^2/ 0.144 = 1000 Ω

Measured Values:

VBattery = 12.28V

IBattery = 11.19 mA = 11.19*10^-3 A
RLoad = 990 Ω
VLoad = 11.01 V

RCableTot = 100.9 Ω

Analysis/Calculations:

Time to Discharge a 0.8Ahr battery capacity circuit:

Amp-Hr = Amps * Time

Time = (0.8 Ahr)/ 11.19*10^-3 A = 71.49.24 hr ≈ 71.49 hr

Distribution Efficiency of Circuit:

Power = V^2/R = I^2*R

PLoad = Pout = I^2*R =  (11.19*10^-3 A)^2 * (990 Ω) = 0.123964 W

PCableTot = PLost =  I^2*R =  (11.19*10^-3 A)^2 * (100.9 Ω) = 0.012634 W

Efficiency = POut/(POut+PLost) * 100 = (0.123964 W)/( 0.123964 W + 0.012634 W) * 100 ≈90.75%

For the resistor box used in this experiment, the power rating of the box is 1 W and the power calculated for PCableTot (the resistor box) is 0.012634 W.  It can be concluded that the experiment did not exceed the power capability of the resistor box since PCableTot is less than the power rating on the resistor box.

The total maximum distance between the battery and the load with a AWG #30 wire:

Maximum Distance  = RCableTot/(2*RAWG#30) = 100.9 Ω/ (2*0.3451 Ω/m) = 146.19 m