The George Washington University
School of Engineering and Applied Science
Department of Electrical and Computer Engineering
ECE 2110 - LAB
Experiment # 3
Voltage Division and Circuit Reduction
Equipment:
Lab Equipment
(2 Sets) Digital Multimeter (DMM)
(2 Pairs) Test Leads
(1 Set) Bread Board
(1 Set) DC Power Supply
Equipment Description
Keithley Model 175 Digital Multimeter (DMM)
Banana to mini-grabber test leads
Prototype Bread Board
Agilent E3631A Triple Output DC Power Supply
Table 1.1
Components:
Symbol Name
Kit Part #
Resistor (R1)
Resistor (R2)
Resistor (R3)
Resistor (R4)
Resistor (R5)
Resistor (R6)
Potentiometer
Green LED Bar
Spice Part
Name
R
R
R
R
R
R
POT
N/A
Part Description
470 Ω Resistor
560 Ω Resistor
680 Ω Resistor
750 Ω Resistor
820 Ω Resistor
910 Ω Resistor
10 k Ω Potentiometer
LED Bar
Table 1.2
(used in schematics
throughout this lab manual)
R1
R2
R3
R4
R5
R6
Objectives:






To calculate and measure the total resistance in a series/parallel circuit.
To calculate and measure the total current in a series/parallel circuit for a given applied
voltage.
To calculate the expected total power dissipated in a series/parallel circuit from nominal
and measured values.
To calculate and measure the voltage drop across and the current through all
components of a series/parallel circuit.
To calculate the power dissipated by each component of a series/parallel circuit from
measured data.
Design, build and test a voltage ladder use a Wheatstone Bridge circuit as a detector of
unknown resistances.
GWU SEAS ECE Department ©2011
ECE 2110 – Experiment #3
Page 1 of 8
Prelab: (Submit electronically prior to lab meeting, also have a printed copy for yourself during lab)
For this prelab, you will simplify circuits to find their equivalent resistance (REQ). The first prelab
problem #1 is solved for you as an example of how to solve problems in part 2.
1. Prelab Problem #1: For the circuit in figure 1, complete steps a-d:
Figure 1 – Circuit to simplify
REQ
a.
In figure #1, find REQ from the perspective of the voltage source V1. REQ is the “load”
attached to the voltage source. Leave REQ in terms of R1, R2, and R3, so we can
substitute numerical values in later. Show all work.
SOLN: Step 1: Remove the voltage source (figure 1a). Simplify the resistors by
determining which are in series and which are in parallel. In this case, they are all in
parallel.
𝑅𝐸𝑄 = 𝑅𝑎 || 𝑅𝑏 || 𝑅𝑐 = (
1
1
1
+
+ )−1
𝑅1 𝑅2 𝑅3
REQ
Figure 1a – Step 1
Figure 1b, step 2
SOLN: Step 2: Generate an equation for REQ in terms of RA, RB, RC. Show the final
circuit as displayed in figure 1b.
b.
For the circuit in figure #1, if V1=6V, find the total current supplied by V1 and the total
power dissipated by the load. Use the numerical values for the resistors from table 1.2.
SOLN: Step 1: Find the total load as seen by V1 by substituting into you REQ equation:
𝑅𝐸𝑄 = 𝑅1 || 𝑅2 || 𝑅3 = (
−1
1
1
1 −1
1
1
1
+
+ ) =(
+
+
) = 185.75 Ω
𝑅1 𝑅2 𝑅3
470 Ω 560 Ω 680 Ω
SOLN: Step 2: Use Ohm’s law to find the total current drawn by REQ:
𝐼1 = (
𝑉1
6𝑉
)=(
) = 32.3 𝑚𝐴
𝑅𝐸𝑄
185.75 Ω
SOLN: Step 3: Find the power dissipated by REQ, by P=IV or P=V2/R or P=I2R
𝑃𝑅𝐸𝑄 = (𝐼1 )(𝑉1) = (32.3𝑚𝐴)(6𝑉) = 194 𝑚𝑊
GWU SEAS ECE Department ©2011
ECE 2110 – Experiment #3
Page 2 of 8
c.
For the circuit in figure #1, calculate the voltage drop across each resistor, the current
through each resistor, and the power dissipated by each resistor.
SOLN: Step 1: The voltage across each resistor is the same for parallel circuits:
12.77mA
6V
6V
10.71mA
8.82 mA
6V
SOLN: Step 2: The current through each resistor is found using Ohm’s law:
IRA = 6 V / 470 Ω = 12.77 mA, IRB = 6 V / 560 Ω = 10.71 mA, IRC = 6 V / 470 Ω = 8.82 mA,
Notice, 12.77 mA + 10.71 mA + 8.82 mA = 32.3mA the total current draw for the circuit!
SOLN: Step 3: The power dissipated by each resistor is found using P=IV or a variant:
PRA = 6V * 12.77 mA = 76.62 mW,
PRB = 6V * 10.71 mA = 64.26 mW,
PRA = 6V * 8.82 mA = 52.92 mW,
Notice the sum of all power is the same as the total power dissipated by REQ! If not,
you’ve made a mistake
d.
For the circuit in figure #1, use PSPICE to find the voltage drop across each resistor, the
current through each resistor, and the power dissipated by each resistor. Record all
values into the table below comparing your hand calculations and spice simulations.
Voltage Drop Across (V)
Calculated
REQ
6V
R1
6V
R2
6V
R3
6V
Simulated
% Error
Measured
% Error
Measured
% Error
Current Through (mA)
Calculated
Simulated
% Error
REQ
R1
R2
R3
GWU SEAS ECE Department ©2011
ECE 2110 – Experiment #3
Page 3 of 8
2. Prelab Problem #2: Using the example solution given for problem #1, for the circuits in figures
2-3, complete steps a-d:
I1
I1
REQ
Fig. 2 – Voltage Ladder Circuit
REQ
Fig. 3 – Series / Parallel Circuit
a.
For each figure (2 & 3), find REQ from the perspective of the voltage source V1. Leave
REQ in terms of R1, R2, R3, R4, R5, and/or R6. Show all work.
b.
For each figure (2 & 3), if V1=6V, find the total current supplied by V1 and the total power
dissipated by REQ. Use the numerical values for the resistors from table 1.2.
c.
For each figure (2 & 3) calculate the voltage drop across each resistor, the current
through each resistor, and the power dissipated by each resistor.
d.
For each figure (2 & 3), use PSPICE to find the voltage drop across each resistor, the
current through each resistor, and the power dissipated by each resistor. Record all
values into a table similar to that shown in problem #1, compare your calculations and
simulations.
GWU SEAS ECE Department ©2011
ECE 2110 – Experiment #3
Page 4 of 8
3. Prelab Problem #3: Consider the figure below for this problem:
VA
VB
Fig. 4 – Wheatstone Bridge Circuit
Figure 4 represents a “Wheatstone bridge.” The purpose of the Wheatstone bridge is to use 3
known resistors (R1, R3, and R4) to find an unknown resistance (R2). We need to generate an
algebraic expression for resistor R2 in terms of the known resistors. Use the following steps to
solve the bridge circuit for R2:
a) Solve for VA in terms of R1, R3, and V1
b) Solve for VB in terms of R2, R4, and V1
(Hint: VA is just the voltage across R3)
(Hint: VB is just the voltage across R4)
The bridge is said to be ‘balanced’ when VA = VB.
c) Set your equations for VA and VB equations equal, solve for R2.
(Hint: V1 will drop out of the equation if you’ve done things correctly)
After step c) is complete, you will have an expression for R2 in terms of R1, R3, and R4. With this
expression, you could build the Wheatstone bridge to find an unknown resistance R 2, if you know
the value of resistors R1, R3, and R4.
GWU SEAS ECE Department ©2011
ECE 2110 – Experiment #3
Page 5 of 8
Lab:
Part I – DC Measurements
In this section, you will construct the circuits in Fig. 1, Fig. 2, and Fig. 3. You will then measure
the voltage and current and calculate the power dissipation of each resistor in the three circuits
given. Use V1 = 6 Vdc.
a. For the circuit in Fig. 1:
1. Construct the circuit in Fig. 1 using a breadboard. DO NOT connect the power
supply (V1) to the circuit yet. Use the DMM to measure the equivalent resistance
(REQ) of Fig. 1.
2. Connect the power supply (V1 = 6 Vdc) to the circuit. Use the DMM to measure the
voltage drop across each resistor.
3. Measure the current through each resistor in the circuit. Note, it is impossible to
measure the current ‘across’ a resistor, you must use the DMM differently
when measuring current. Ask you GTA how if you do not remember.
4. Measure the total current (I1) used by the circuit.
5. Find the power dissipated by each resistor.
6. Record all data using a table similar to those used in the prelab. Make sure to
properly label your tables.
b. For the circuit in Fig. 2:
1. Construct the circuit in Fig. 2 using a breadboard. DO NOT connect the power
supply (V1) to the circuit yet. Use the DMM to measure the equivalent resistance
(REQ) of Fig. 2.
2. Connect the power supply (V1 = 6 Vdc) to the circuit. Use the DMM to measure the
voltage drop across each resistor.
3. Measure the current through each resistor in the circuit. Note, it is impossible to
measure the current ‘across’ a resistor, you must use the DMM differently
when measuring current. Ask you GTA how if you do not remember.
4. Measure the total current (I1) used by the circuit.
5. Find the power dissipated by each resistor.
6. Record all data using a table similar to those used in the prelab. Make sure to
properly label your tables.
c. For the circuit in Fig. 3:
1. Construct the circuit in Fig. 3. DO NOT connect the power supply (V1) to the circuit
yet. Use the DMM to measure the equivalent resistance (REQ) of Fig. 3.
2. Connect the power supply (V1 = 6 Vdc) to the circuit. Use the DMM to measure the
voltage drop across each resistor.
3. Measure the current through each resistor in the circuit.
4. Measure the total current (I1) used by the circuit.
5. Find the power dissipated by each resistor.
6. Record all data using a table similar to those used in the prelab.
GWU SEAS ECE Department ©2011
ECE 2110 – Experiment #3
Page 6 of 8
Part II – Design, Build and Test the Voltage Ladder
In this section, you are asked to design a voltage ladder using the concept of Voltage Division.
Use the circuit in Fig. 2 and find the appropriate values for R1, R2, R3, and R4 to build a voltage
ladder with the following specifications (note: R1, R2, R3, and R4 are for you to calculate, do not
use the values from the table):
Total Power Consumed (Ptotal): ≤ 0.14 Watts (DC)
Power Supply (V1): 6 Vdc ±5%
VAB: 0.115 Volts (DC) ±5%
VBC: 0.115 Volts (DC) ±5%
VCD: 2.30 Volts (DC) ±5%
VDE: 3.45 Volts (DC) ±5%
Hint: A good first step would be to examine the relationship between V1, Ptotal, and total current.
After completing your voltage ladder, you will connect the circuit to your green LED bar at points
B, C, and D according to figure 2 (your GTA will assist you if necessary). In turn, these LEDs will
connect directly to ground. Vary the supply voltage from 0 V to 6 V (feel free to experiment).
What happens to the intensity of the LEDs as you vary the supply voltage? Do you notice
a pattern?
Demonstrate this circuit to your GTA.
GWU SEAS ECE Department ©2011
ECE 2110 – Experiment #3
Page 7 of 8
Part III – Wheatstone Bridge
Consider the Wheatstone bridge in figure 5:
a) Build a Wheatstone Bridge, you will need:
 R1 = 2 kΩ, R3 = 5 kΩ, R4 =4 kΩ
 R2 = 10 kΩ potentiometer
 Voltmeter (DMM 175) to measure voltage drop between nodes A and B (VAB)
Figure 5: Wheatstone Bridge
a) Once you have completed the setup, connect a 6 volt supply as indicated in figure 5.
Record the value of VAB.
b) Adjust the potentiometer until the bridge is ‘balanced.’ (hint: see the prelab #3 to see
what balanced means for a Wheatstone bridge circuit.) Record VAB.
c) Once you have balanced the bridge, calculate the value of the potentiometer using the
expression you derived for R2 in the prelab – question #3. Show your calculation.
d) Now remove the potentiometer from the circuit and without adjusting it, use the DMM to
measure its actual value. Record the value of R2.
Part IV – Analysis questions for your lab write-up
For part 1 of the lab: Compare and contrast the calculated results from your prelab, to your
SPICE simulations and finally to the DC measurements made in the lab itself. Show the
percentage error in each case. Explain the differences between the calculated, measured, and
simulated results then include a discussion on the reason for the discrepancies. Also explain the
concept of tolerance in all the devices and equipment and how to compensate for the problem of
inaccurate measurements.
For part 2 of the lab: Make sure to answer all questions asked in tandem with the lab instructions.
Now that you have designed and observed the behavior of a voltage ladder / LED bar
combination in detail, can you think of any applications for such a circuit? Name one or two
possibilities in your report.
For part 3 of the Lab: Why does the bridge have to be ‘balanced’ in order to calculate the value of
R2? Does your calculated value for R2 (from step 3 c) match your measured value of R2 (from
step 3 d), what is the % error? Research and explain several uses of the Wheatstone bridge.
GWU SEAS ECE Department ©2011
ECE 2110 – Experiment #3
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