LAB #06: Mesh Analysis II

OVERVIEW:
The purpose of this lab was to analyze, build, and test a circuit with multiple sources. Once again, we will solve the circuit using mesh analysis.

PROCEDURE:
Pre-Lab:
As illustrated in the ENGR 44 Lab book, we will analyze the circuit in Figure 1 using mesh analysis techniques to determine the mesh currents; and predict the voltage differences V1 and V2 using those mesh currents. Please note that this is essentially the same circuit used in my Nodal Analysis II lab.

Lab:

1. Construct the circuit; measure and record all actual resistance values. Measure V1, V2, and I1 in the circuit.
2. Calculate the percentage error between your measured values and your predicted values for V1 and V2 respectively.

Actual Circuit Built

ANALYSIS:
Pre-Lab:
Predicted Voltage Values:
V1 = 4.999 V
V2 = 1.224 V

Predicted Current Values:

i1 = .0604 mA
i2 = I1 = -0.3208 mA
i3 = -1.056 mA

Pre-Lab Calculations w/ Circuit Diagram

Lab:

Part 1:
Actual Resistance Values:

R1 = 20 k
R2 = 4.7 k
R3 = 10 k
R4 = 6.8 k

Actual Voltage Values:
V1 = 4.98 V
V2 = 1.23 V

Actual Current Values:
I1 = -0.366 mA
i1 = 0.066 mA

i1 on DMM

Part 2:
Percent error between predicted and measured voltage:
Error in V1: (|4.999 - 4.98| / 4.999)* 100 = 0.380%
Error in V2: (|1.224 - 1.23| / 1.224)* 100 = 0.490%

CONCLUSION:
Our measured values for V1 and V2 are definitely within a reasonable margin of error. During the pre-lab, we used mesh analysis to predict the values of V1 and V2. We found these values to be 4.999 V and 1.224 V respectively. For the actual lab, we measured Vl = 4.98 V and V2 = 1.23 V. This corresponds to a percent error of 0.380% and 0.490%  for V1 and V2 respectively. This uncertainty is likely due to the internal resistance of the DMM.

LAB #05: Mesh Analysis

OVERVIEW:
The purpose of this lab was to analyze, build, and test a circuit with multiple sources. This time, we will solve the circuit using mesh analysis.

PROCEDURE:
Pre-Lab:
As illustrated in the ENGR 44 Lab book, we will analyze the circuit in Figure 1 using mesh analysis techniques to determine the voltage differences V1 and V2. Please note that this is essentially the same circuit used in my Nodal Analysis lab.

Lab:

1. Construct the circuit; measure and record all actual resistance values. Measure V1 and V2 in the circuit.
2. Calculate the percentage error between your measured values and your predicted values for V1 and V2 respectively.

Physical Circuit (Zoomed In)

Physical Circuit (Zoomed Out)

ANALYSIS:
Pre-Lab:
Predicted Voltage Values:
V1 = 2.356 V
V2 = 4.356 V

Pre-Lab Calculations on Whiteboard

Lab:
Part 1:
Actual Resistance Values:

R1 = 10 k
R2 = 20 k
R3 = 6.8k

Actual Voltage Values:
V1 = 2.34 V
V2 = 4.32 V

V1 on DMM

V2 on DMM

Part 2:
Percent error between predicted and measured voltage:
Error in V1: (|2.356 - 2.34| / 2.356)* 100 = 0.679%
Error in V2: (|4.356 - 4.32| / 4.356)* 100 = 0.826%

CONCLUSION:
Our measured values for V1 and V2 are definitely within a reasonable margin of error. During the pre-lab, we used mesh analysis to predict the values of V1 and V2. We found these values to be 2.356 V and 4.356 V respectively. For the actual lab, we measured Vl = 2.34 V and V2 = 4.32 V. This corresponds to a percent error of 0.679% and 0.826%  for V1 and V2 respectively. This uncertainty is likely due to the internal resistance of the DMM.

LAB #03: Nodal Analysis

OVERVIEW:
The purpose of this lab was to analyze, build, and test a circuit containing multiple sources. Our method for solving the circuit is nodal analysis.

PROCEDURE:
Pre-Lab:
As illustrated in the ENGR 44 Lab book, analyze the circuit in Figure 1 using nodal analysis to predict the values of V1 and V2.

Lab:

1. Construct the circuit; measure and record all actual resistance values. Measure V1 and V2 in the circuit.
2. Calculate the percentage error between your measured values and your predicted values for V1 and V2 respectively.

Physical Circuit (Zoomed In)

Physical Circuit (Zoomed Out)

ANALYSIS:
Pre-Lab:
Predicted Voltage Values:
Va = -0.602 V
V1 = 2.397 V
V2 = 4.397 V

Pre-Lab Calculations w/ Circuit Schematic

Lab:
Part 1:
Actual Resistance Values:

R1 = 9.9 k
R2 = 21.7 k
R3 = 6.6 k

Actual Voltage Values:
V1 = 2.38 V
V2 = 4.35 V

Measuring V2 (Sample)

V1 on DMM

V2 on DMM

Part 2:
Percent error between predicted and measured voltage:
Error in V1: (|2.397 - 2.38| / 2.397)* 100 = 0.709%
Error in V2: (|4.397 - 4.35| / 4.397)* 100 = 1.07%

CONCLUSION:
Our measured values for V1 and V2 are definitely within a reasonable margin of error. During the pre-lab, we used nodal analysis to predict the values of V1 and V2. We found these values to be 2.397 V and 4.397 V respectively. For the actual lab, we measured Vl = 2.38 V and V2 = 4.35 V. This corresponds to a percent error of 0.709% and 1.07%  for V1 and V2 respectively. This uncertainty is likely due to the internal resistance of the DMM.

LAB #04: Nodal Analysis III

OVERVIEW:
The purpose of this lab was to analyze, build, and test a circuit with multiple sources. Once again, we use nodal analysis as our primary solving technique.

PROCEDURE:
Pre-Lab:
As illustrated in the ENGR 44 Lab book, use nodal analysis techniques to analyze the circuit in Figure 1 to determine the voltage difference V1 and current I1.

Lab:

1. Construct the circuit given in the lab book, measure V1 and I1 using DMM.
2. Calculate the percent difference between your predicted values and measured values.

Physical Circuit (Zoomed In)

Physical Circuit (Zoomed Out)

ANALYSIS:
Pre-Lab:
Predicted Voltage and Current Values:
A) V1 = 2.344 V
B) I1 = 0.287 V

Pre-Lab Calculations w/ Circuit Schematic

Lab:
Part 1:
Actual Resistance Values:

R1 = 1.20 k
R2 = 4.63 k
R3 = 6.73 k
R4 = 21.8 k

Actual Voltage  and Current Values:
V1 = 2.34 V
I1 =  0.28 V

V1 measured on DMM

Part 2:
Percent error between predicted and measured voltage:
Error in V1: (|2.344 - 2.34| / 2.344)* 100 = 0.171%
Error in I1: (|0.287 - 0.28| / 0.287)* 100 = 2.44%

CONCLUSION:
Our measured values for the voltage difference V1 and current I1 matched closely to their corresponding predicted values. During the pre-lab, we used nodal analysis to predict the values of V1 and I1 and we found these values to be 2.344 V and 0.287 mA respectively. For the actual lab, we measured Vl = 2.34 V and I1 = 0.28 mA, which corresponds to a percent error of 0.171% and 2.44%  for V1 and I1 respectively. This uncertainty is likely due to the internal resistance of the DMM, which may have caused our measured voltage, current, and resistance values to be slightly off.

LAB #02: Practical Voltage & Current Measurement

OVERVIEW:
The purpose of this lab was to explore how non-ideal meters affect our measurements of voltage and current in a physical circuit.

PROCEDURE:
Pre-Lab:
As illustrated in the ENGR 44 Lab book, analyze the circuit in Figure 1 to determine the value of voltage Vout for the cases in which:

1. Vout is determined using an ideal voltmeter.
2. Vout is determined using a non-ideal voltmeter of internal resistance Rm.

Lab:

1. Construct the circuit given in the lab book, measure Vout using DMM, and use pre-lab results to estimate the internal resistance of DMM.
2. Repeat step 1, but use the Analog Discovery  module to measure Vout instead; as well as determine the internal resistance of the scope instrument.

Physical Circuit: Two 10MΩ resistors in series

ANALYSIS:
Pre-Lab:
A) Vout = 2.5 V
B) Vout = (Rm / (10MΩ + 2Rm))*5V

Pre-Lab Calculations

Lab:
Part 1:
Vout (DMM) = 1.66V
Rm = 10MΩ

Part 2:
Vout (scope) = 2.5V
Rm = infinity Ω

Scope Reading

CONCLUSION:
In part 1, we measured Vout to be 1.66V using the DMM. This value makes sense because it implies that the internal resistance, Rm of the DMM is approximately 10MΩ, which is common for many digital meters today. For part 2, we measured Vout to be 2.5V using the Analog Discovery Module. This value is promising, yet misleading because it implies that the Analog Discovery Module has infinite resistance, thereby allowing Vout to be exactly half of the input voltage like our calculations predicted. This, however, is improbable because we should expect physical meters to have a high, yet measureable internal resistance.