Answer & Explanation:lab reportOne of the attachment is the requirement. There is an attachment will be post it soon << which are the tables. img_4730.jpg lab2_equivalentresistance_kvl_kcl.pdf lab2_equivalentresistance_kvl_kcl_requirements.pdf Unformatted Attachment Preview MORGAN STATE UNIVERSITY DEPARTMENT OF ELECTRICAL AND COMPUTER ENGINEERING EEGR 203: INTRODUCTION TO ELECTRICAL LABORATORY Instructor: Dr. Gregory M. Wilkins LAB 2: Equivalent Resistance and Kirchoffs Voltage and Current Laws You will see this reminder in all of your labs. Please take notes and commit all you learn in each lab to memory You will need every bit of this information to complete your project !!! Educational Objective: The intent of this laboratory is to introduce the student to Kirchoffs Voltage and Current Laws and equivalent resistance. You will also have an introduction to your final laboratory project. Introduction: Kirchoffs Voltage Law (KVL) states that the sum of voltage around any loop is equal to zero. Consider the single loop of Figure 1. Applying KVL: KVL for series resistors Vs V2 V3 V1 = 0 ? Vs = V1+ V2 + V3 ? Vs = IsR1 + IsR2 + IsR3 ? Vs = (R1 + R2 + R3) Is ? Req = R1 + R2 + R3 Figure 1 SINGLE, LOOP Note that individual resistors in series may be replaced with a single resistor equal to the sum of the individual resistors. This is a direct extension of the Kirchoffs law. 1 Kirchoffs current law Kirchoffs current law (KCL) states that the sum of the currents leaving a node equals zero, or alternately, the sum of the currents entering a node equal zero, or the sum of currents entering equal the sum of currents leaving a node. Consider the single node circuit illustrated in Figure 2. KCL for parallel resistors ? ? Is - I1 - I2 - I3 = 0 ?Is = I1 + I2+I3 ?Is = V / R1 + V / R2 + V / R3 Is = V (1 / R1 + 1/ R2 + 1 / R3) Is / V = 1 / Req = 1 / R1 + 1 / R2 + 1 / R3 Note that the equivalent resistance seen by the voltage source is: Req = 1 / (1 / R1 + 1 / R2 + 1 / R3) For the special case of two resistors in parallel: Req =(R1 * R2)/ (R1 + R2) Figure 2 SINGLE NODE This is commonly called product over sum. Note that for the three resistors, the equivalent is not equal to the product of the three divided by the sum of the three. Consider Figure 3. 2 R4 A R3 B 1.5k? 330? R1 560? Vs 5V D Figure 3 Configuration of various resistors Analysis: For Mesh 1: KVL Vs I4*R4 - I1* R1 = 0 or Vs = I4*R4 + I1*R1 For Mesh 2: KVL I1*R1 - I3*R3 I2*R2 = 0 Node B: KCL I4 I1 I3 =0 or I4 = I1 + I3 Node C: KCL I3 I2 = 0 or I3 = I2 We now have four equations and four unknowns. 3 C R2 180? Equipment: Digital Multi-meter 6038 System Power Supply Discrete Resistors as necessary Decade Resistor Box Procedure: 1. Set up each of the resistor arrangements as illustrated in Figure 4 using discrete resistors. For each arrangement use an ohmmeter to measure the resistance between points X -Y and record your results in Table 1. 2. See Figure 4 A,B,C. Apply a nominal 5V source across terminals x and y with ground at terminal y.(Remember to limit the current to100mA ) Measure the current entering terminal x and record your values in Table 1. 3. Replace each of the resistor combinations in Figure 4 A, B, and C by their equivalent resistance (use a decade box ) and repeat step 2 record your values in Table 1. 4. Build the circuit illustrated in Figure 3. Limit the current supply to 100 m
A and adjust the
voltage supply to 5.0 V. Measure the following: VR1, VR2, VR3, VR4, VA, VB, and VC. Record
your values in Table 2. Note the polarities of all the voltages. Measure the following
currents: I1, I2, I3, and I4 record them in Table 2 and note their polarities.
x
R1
820?
R2
680?
y
Figure 4A Series configuration (R1, R2)
4
x
R1
5.6k?
R3
8.2k?
R2
4.7k?
y
Figure 4B Series configuration (R1, R2) in parallel with R3
R1
x
680?
R2
8.2k?
R3
8.2k?
y
Figure 4C Configuration with R1 in series with parallel configuration (R2,R3)
5
Pre-Lab:
1.
2.
3.
Compute the equivalent resistance for each of the resistor combinations of Figure 4.
Compute the current entering terminal x of each of the resistor networks of Figure 4 if a 5.0 Volt DC
supply is connected across terminal x and y.
Compute the theoretical voltage and current values for each of the measurements in Table 2. Show
all details of your work. Record theoretical calculations in the appropriate spaces in Table 2.
RESULTS
1.
2.
Show from the theoretical and experimental results Table 2 that the algebraic sum of the voltages
around the three loops of the circuit of Figure 3 are equal to zero. Note that there are two inner
loops and one outer loop.
Show that the algebraic sum of the currents entering node B of Figure 3 is equal to zero by using
the data of Table 2.
Discuss and explain any discrepancies between the experimental and theoretical results. Calculate the
percentage error between all experimental and theoretical results, with the theoretical results as your
nominal value.
Table 1 — Equivalent Resistance — Steps 1,2,3
Circuit A
Circuit B
Circuit C
Theoretical Resistance,
values from resistor
makings (?)
Theoretical Current with 5V
Source
Resistance measurement
using ohmmeter (?)
Current measurement with
5V Source
Decade box resistance
Current through decade box
Table 2 — Kirchoff’s Current and Voltage Laws
VR1
VR2
VR3
VR4
VA
VB
VC
I1
I2
I3
I4
MEAS.
Theor.
Error%
6
EEGR 203: Introduction to Electrical Laboratory
Report Requirements for Lab 2
Equivalent Resistance and Kirchoffs Voltage and Current Laws
Be sure to include ALL of the following information in your lab report.
1. For Table 1 Equivalent Resistance, show the work required to obtain the theoretical values
of resistance and current for each configuration.
2. Make sure that all measurements have been included for Table 1.
3. For Table 2 Kirchoffs Current and Voltage Laws, show the work required to obtain the
theoretical values for ALL entries in the table. This should include, at a minimum, KVL for
two loops and KCL for two nodes. This will produce four equations for the four current
unknowns I1, I2, I3, and I4. Try to reduce the results to two equations for the two unknowns I1
and I2. Once the currents are obtained, all unknowns should be readily obtainable.
4. Show from the theoretical and experimental results in Table 2 that the algebraic sum of the
voltages around the three loops of the circuit of Figure 3 are equal to zero. Note that there
are two inner loops and one outer loop.
5. Show that the algebraic sum of the currents entering node B of Figure 3 is equal to zero by
using the data of Table 2.
6. Discuss and explain any discrepancies between the experimental and theoretical results.
Calculate the percentage error between all experimental and theoretical results, with the
theoretical results as your nominal value.
…
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