# LABORATORY EXPERIMENT #2

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```					                             LABORATORY EXPERIMENT #2

“RESISTANCE MEASUREMENTS AND INTRODUCTION TO ELECTRONICS
WORKBENCH”

Discussion: In this lab we will investigate the different types of resistors available and their
usage in circuits. We will then build various resistive networks with different gauge wire and
compare the response of these networks loading with lamps and speakers. Series and parallel
resistive circuits will be built and measured on the proto-boards and the use of fuses will be
introduced. These resistive networks will be simulated on the Electronics Workbench software
Educational Version 2001 and their response will be compared to the actual values measured
from the test circuits.

Section A. Wire Gauge, Resistivity, and Resistance Measurement

The following types of resistors are common:

   Carbon composition-moderate stability 0-60oC-Resistance increases above and below this
temperature range, non-inductive, noisy, wide tolerances.
   Wire wound-stable, close tolerances, inductive.
   Metal film-exceptionally stable, close tolerances, non-inductive, little noise, power
limited to 3W.
   Carbon film-stable, non-inductive, negative temp coefficient.
   Potentiometers-available with linear or log taper, can be noisy.

Resistance is calculated by the equation, R = L/A, where R is the resistance in ohms,  is the
resistivity in ohm-meters, L is the length of the wire in meters, and A is the cross sectional area
of the wire in meters2. Wires typically have a circular cross section and a standard system for
describing various wire sizes is in use. This system describes wires by its Gauge (AWG).

Thumb rules:
   Small gauge refers to large wires and large gauge refers to small wires.
   Radius or diameter increases by 12.3% for each one-gauge size reduction.

A 28-gauge to 26-gauge is considered a 2-gauge size reduction.

   A 6-gauge size reduction is a doubling of cross sectional area (and current carrying
capacity).
   A 4-gauge size reduction increases the cross sectional area by 59%.
   A 2-gauge size reduction increases the cross sectional area by 26%.

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Below is a chart with copper wire electrical values.

Copper Wire Electrical Values

Wire            Diameter         Area (mm2)        Max Current @ 250
Gauge            (mm)                                   C (A)
10               2.588                5.2604           14.83
12               2.053                3.3103            9.33
14               1.628                2.0816            5.87
16               1.291                1.3090            3.69
18               1.024                0.8235            2.32
20               0.812                0.5178            1.46
22               0.644                0.3257            0.91
24               0.511                0.2051            0.58
26               0.405                0.1288            0.36
28               0.321                0.0809            0.23
30               0.255                0.0511            0.14

for copper @ 250C is 1.733 x 10-8 -m

Wire Gauge Exercise: (Caution: the wires on the spools are delicate, attach the leads gently)

1. Take a 40-foot spool of number 22-gauge wire and measure its resistance with the
handheld multimeter and the bench top multimeter. Record each value.

R 22 Gauge handheld multimeter = ___________________

R 22 Gauge bench top multimeter = ___________________

2. Take a 75-foot spool of number 26-gauge wire and measure its resistance with the
handheld multimeter and the bench top multimeter. Record each value.

R 26 Gauge handheld multimeter = ___________________

R 26 Gauge bench top multimeter = ___________________

3. Take a 200-foot spool of number 30-gauge wire and measure its resistance with the
handheld multimeter and the bench top multimeter. Record each value.

R 30 Gauge handheld multimeter = ___________________

R 30 Gauge bench top multimeter = ___________________

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4. Connect the function generator to the oscilloscope and setup a 2000 Hz sine wave pattern
with 5 VDC peak-to-peak. Connect the function generator to the speaker with the 22-
gauge and 30-gauge coils of wire and record the qualitative difference in the sound
below.

_______________________________________________________________________

_______________________________________________________________________

_______________________________________________________________________

5. Calculate the expected resistance of the wires using the gauge values and standard
resistivity values for copper. Compare these results to the measured and recorded values
above from each of the meters. Which meter reading is likely to be more accurate at low
resistance values?

_______________________________________________________________________

_______________________________________________________________________

Use the measured values for the 200-foot 30-Gauge wire to calculate  for copper. What
errors may affect the measured results? Show your work and answers below.

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Section B. Series and Parallel Circuit Resistance Measurement

1. In class we derived the series and parallel equivalent resistance formulas by using test
circuits and Ohm’s Law. Now we will verify experimentally confirm those formulas by
measuring the resistance of various series, parallel, and combination circuits. Collect the
components to build the circuit in Fig 1a. Measure each resistor to obtain the most
precise and accurate value.

R 10 = ___________________

R 51 = ___________________

R 220 = ___________________

R 1.5k = ___________________

R 3.6k = ___________________

10                 51

R1                  R2

5% Tolerance Resistors           R3   220 
R5                  R4

3.6k               1.5k 
Figure 1a. Series Resistor Nework

Fill in the following chart. Calculate the manufacturer's allowable high and low tolerance
values.

Resistor         Measured            Tolerance       Tolerance
Value                High            Low
R 22
R 51
R 220
R 1.5k
R 3.6k

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What is the worst case high equivalent resistance? _________________________________

What is the worst case low equivalent resistance? __________________________________

Build the circuit and measure the equivalent resistance. _____________________________

Is the equivalent resistance within the expected tolerance? ___________________________

1. Collect the components to build the circuit in Fig 1b. Measure each resistor to obtain the
most precise and accurate value.

R 51 = ___________________

R 220 = ___________________

R 1.5k = ___________________

R 3.6k = ___________________

51 

R2
220      1.5k       3.6k 
R3         R4         R5
5% Tolerance

Figure 1b Parallel-Series Resistor Network

2. Fill in the following chart. Calculate the manufacturer's allowable high and low tolerance
values.

Resistor         Measured          Tolerance         Tolerance
Value              High              Low
R 51
R 220
R 1.5k
R 3.6k

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What is the worst case high equivalent resistance? _________________________________

What is the worst case low equivalent resistance? __________________________________

Build the circuit and measure the equivalent resistance. _____________________________

Is the equivalent resistance within the expected tolerance? ___________________________

What value resistor would you add in parallel to this circuit to reduce the equivalent
resistance to 100? Show your work below.
__________________________________

3. Use 6V, 100mA nominal test lamps to build the following:

   A series system of three lamps where each lamp is running at 85% of rated voltage.
   A parallel system of three lamps running at 85% of rated voltage.

4. Use a single test lamp to collect the voltage/current relationship for the bulb. Take
voltage and current measurements in 0.5V or smaller steps up to rated voltage. Plot the
results on a separated sheet and determine if the bulb has a positive, negative or no
temperature coefficient or resistance.

INSTRUCTOR VERIFICATION: _________________

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Lamp Voltage (V)   Lamp Current (A)   Lamp Resistance ()

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Section C. Electronics Workbench Introduction

Note: Each member of the group should complete this section independently at least once.
The Laboratory Practical will require each student to be proficient in the tasks
outlined in this section.

1. Log on to your computers and open Multisim, the Electronics Workbench package.
Select the options menu and preferences sub-menu. Under the circuit tab ensure the
following are checked:

   Show component labels
   Show component reference ID’s
   Show node names
   Show component values
   Show component attribute, then click OK

2. Under the workspace tab ensure the following are checked:

 Show grid, then click OK

3. Under the Component Bin tab ensure the following are checked:

 ANSI
 No auto show, click to open
 Continuous placement for multi-section part only (ESC to quit), then click OK

4. Under the font tab ensure the following are checked:

 Change all - all selections checked
 Apply to entire circuit, then click OK

5. Select place and then the place component sub-menu. Data name should be Multisim
Master. Select the component family Resistor and click OK. Select the required resistor
from the Component Name List, (430Ohm_5%), click OK and use the mouse to position
the component in the proper area of the circuit. Click again to anchor the component.
Further clicking on the component will select it for movement or editing. The component
can be flipped by selecting edit or right clicking the mouse when the component is
selected. In the edit menu, value tab, the component value can be changed in the master
database. The fault tab allows open, short, or leakage faults to be defined.

6. Select a (3.3kOhm_5%) resistor and place it on the same level, but to the right of the
430 resistor. Position the mouse pointer at the right side of the 430 resistor and click
and drag a wire connection to the left side of the 3.3k resistor. A broken line will
indicate the proposed connection path. Click again when the proposed connection
reaches the next component and the line will change from broken to solid indicating a

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wire connection has been placed. A node number should also be near the wire to identify
the connection. In complicated wiring, crossed wires will only connect if a connection
dot is added, otherwise the wires cross each other without a connection.

7. Select a (22kOhm_5%) resistor and a (110kOhm_5%) resistor and place them in series
with the other two resistors in a pattern that duplicates Circuit 1. Place a ground as
shown. Don’t be concerned if the node numbering is different than the example circuit.

Circuit 1

8. Select the Simulate menu, Instruments sub-menu, and click on multimeter. Place the
multimeter to the left of the circuit and click to anchor. Double click the multimeter to
reveal the multimeter controls which will be identified by the meter’s number (XMM1,
XMM2, etc.). Wire the meter into the circuit. Note the polarity of the meter leads, and
connect voltmeters and ohmmeters in PARALLEL and ammeters in SERIES. Wire
this meter as an ohmmeter to test the net equivalent series resistance of the circuit. To
simulate and get the multimeter to readout toggle the simulate switch in the upper right
corner to 'On' (line side pushed in, circle side out). The circuit should readout about
132.760k.

9. Now modify the above circuit by adding a battery and an ammeter as shown in Circuit 2.
Select place and add the battery from the Component Name List, DC Voltage Source,
click OK and use the mouse to position the component in the proper area of the circuit.
Click again to anchor the component. Edit the battery voltage to 5 VDC. To do this
highlight the battery by clicking on it, then select edit component properties. Adjust the
voltage value to the desired value and click OK. Add the ammeter. Select the Simulate
menu, Instruments sub-menu, and click on multimeter. Place the multimeter to the
middle of the circuit and click to anchor. Click on the wire between R1 and R2 and
delete it. Double click the multimeter to reveal the multimeter controls which will be
identified by the meter's number (XMM1, XMM2, etc.). Wire the meter into the circuit.
Note the polarity of the meter leads, and connect voltmeters and ohmmeters in
PARALLEL and ammeters in SERIES. Wire this meter as an ammeter to test the net
equivalent current of the circuit. To simulate and get the multimeters to readout toggle
the simulate switch in the upper right corner to 'On' (line side pushed in, circle side out).

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10. Now we will simulate for all the node voltages for Circuit 2. Select Simulate, Analyses,
DC Operating Point, Output Variables tab and sub-menus respectively. Chose All
Variables and transfer each variable to the right side so that it is selected for analysis.
Click simulate and a DC operating point chart will show the node voltages and net circuit
current.

Circuit 2

11. Show the Instructor you can place a 20A Fuse in series for protection of Circuit 2.

INSTRUCTOR VERIFICATION: _________________

Post-Lab Exercises

1. A public address speaker system running a nominal 200W at 40VDC with an 8 speaker is
having it's wiring extended to reach another part of the room. The current hookup wire
length is negligible, but the new run will add 300m to the run. To have 100W available at
the speaker, what size copper wire at 25C should I choose for the job?

2. Why is bare wire allowed to have more current pass through it than insulated wire in the
National Electrical Code (NEC) Standards?

3. If a resistor failed in a circuit, would you rather have it fail as a short-circuit or an open-
circuit and why?

4. If you were sending electrical power from Moss Landing to Los Angeles, would you use low
voltage high current or high voltage low current? Why does it make a difference to the
power producer and end user?

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