Subsections
The purpose of this first laboratory assignment is to review
fundamental concepts and to extend your DC circuit analysis
skills. The assignment draws from the first four chapters of your text
and guides you through the production of a your own reference on the
analysis of circuits containing resistor networks, ideal voltage
sources, and ideal current sources. Resistor networks are not very
exciting to build, so much of our work will be theoretical. A
secondary goal of this assignment is to introduce you to the Berkeley
Spice circuit simulation program in a context in which you can easily
verify results by hand.
Collect definitions for the following fundamental physical quantities,
devices, and concepts.
Charge, Current, Voltage, Ground, Energy,
Power, Resistance, Conductance, Resistor, Ideal Voltage Source, Ideal
Current Source, Passive Sign Convention, Node, Essential Node, Branch,
Loop, Mesh, and Planar Circuit.
Also consider what is meant by the phrases ``voltage across device X''
and ``voltage at point A.''
I don't expect you to come up with these on your own, but acknowledge
^{1}
the resources you use. We will discuss these in class.
``Ohmic'' devices show a linear relationship between applied voltage
and current,

(1) 
This is known as Ohm's Law and applies to standard resistors
and wires, among other things.
Experiment :
Light bulbs are often thought of as resistors, but they are rumored to
be nonlinear. That is, they are alleged to be non ohmic. Test this
hypothesis experimentally with the light bulb supplied. (Lew will
provide requested equipment, if we own it.) Choose a resistor (from
one of the resistor boxes on the table at the west end of the lab) of
similar resistance to the light bulb, and test it as well for
comparison.
Give a written description of your experiment and results.
 ...Stated
Construct, in your own words, statements
of Kirchoff's Laws. (Acknowledge the resources you use.)
 ...Applied to Voltage and Current Dividers
Apply Kirchoff's Laws to the circuits shown in Figure 1 to
derive equations for the voltages and across the resistors
in the ``voltage divider'' circuit (a) and for the currents and
through the resistors in the ``current divider'' circuit (b).
 ...Applied to a Circuit with Two Loops
Design and
solve a problem involving a circuit containing resistors, a single
ideal voltage supply, and two loops. We will exchange problems as an
exercise in class.
 Resistors in Series and Parallel
Apply Kirchoff's Laws to circuits (a) and (b) in
Figure 1 to derive the well known equations for the
equivalent resistance of two resistors in series and in parallel.
In each case, consider the special cases , ,
and .
 Exercises
Find the equivalent resistance of the networks of resistors (c) and
(d) in Figure 1, using , , and 50 for unlabeled resistors.
Figure 1:
(a) and (b) are simple (simplest) circuits
with two resistors connected in series and parallel, respectively. (c)
and (d) are resistor networks.

 Y Transformations
Practice working with DeltaWye (Y) transformations by
finding the equivalent resistance of the resistor networks (a) and (b)
in Figure 2.
Figure 2:
Resistor networks requiring Y
transformations. , unlabeled resistors are
1 k.
(a)
(b)

 Experiment
Build the resistor network shown in Figure 2(a) and
check your calculation of its equivalent resistance experimentally.
Methods of Circuit Analysis
 The Node Voltage Method
Construct, in your own words, a step by step description of the Node
Voltage Method of circuit analysis. Include an example circuit
diagram. (Acknowledge the resources you use.)
 The Mesh Current Method
Construct, in your own words, a step by step description of the Mesh
Current Method of circuit analysis. Include an example circuit
diagram. (Acknowledge the resources you use.)
 Exercises
Find the unknown currents and voltages for circuits (a)  (d) in
Figure 3 using both the node voltage and mesh
current methods.
Figure 3:
DC circuits with resistor networks and
power supplies.

Use Spice to verify your calculations of
Section 3. Hand in printouts of your circuit files
and output. However, do not assume that they speak for
themselves. Summarize important results.
Just as networks of resistors between two nodes may be replaced by a
single equivalent resistance, entire circuits can be replaced by a
combination of a single resistor and an ideal power source in two
ways.
 Thevenin Equivalent Circuits
Construct, in your own words, a step by step method of finding the
Thevenin equivalent voltage and resistance. Include an example circuit
diagram. (Acknowledge the resources you use.)
 Norton Equivalent Circuits
Construct, in your own words, a step by step method of finding the
Norton equivalent current and resistance. Include an example circuit
diagram. (Acknowledge the resources you use.)
 Exercises
Find the Thevenin and Norton equivalent circuits for terminals A and B
of circuits (a) and (b) in Figure 4.
Figure 4:
Circuits to be replaced with Thevenin and
Norton equivalent circuits for terminals A and B.

 Experiment
Build the circuit shown in Figure 4(a), and check your
predictions for the voltage across and current through a 500
load resistor.
Most resistors you will encounter are marked with a set of bands,
according to a standard color code, which you can use to determine
their resistances. There are ten colors corresponding to numerical
digits 09 (see the table below), and gold and silver bands indicating
5% and 10% accuracy in the coded resistance, respectively. Starting
at the far end of the resistor from the gold/silver band, the first
two bands are the first two digits in the resistance. The third band
gives the power of ten by which you multiply the first two digits to
obtain the resistance.
color 
black 
brown 
red 
orange 
yellow 
green 
blue 
violet 
gray 
white 

digit 
0 
1 
2 
3 
4 
5 
6 
7 
8 
9 

multiplier 
1 
10 
100 
1k 
10k 
100k 
1M 
10M 
100M 
1000M 

For example, Blue Yellow Red Gold gives
with a tolerance of 5%, or
.
Copyright © 20012004, Lewis A. Riley

Updated Mon Jan 19 13:29:10 2004

This work is licensed under a Creative Commons License.