Lab 5: BASIC CIRCUITS ( Resistors, Voltage, and Current with MATLAB adapted from P-178 DC Circuit Labs ) Introduction : Electric circuits can be defined as closed or continuous paths in which electric currents are confined and around which electric currents can be caused to flow. Electrical circuits are an essential part of daily living, and may be found in heavy and light industry, commercial installations and operations, and residential applications. Modern life and its many conveniences seem inconceivable without the use of electric circuits. The total resistance of a circuit is the sum of the individual resistances of the power source, the wiring, and the load. The load resistance is generally much higher than either the resistance of the power source or the wiring. The resistances of the wiring are usually neglected in classroom laboratory experiments. Very rarely is circuit wiring significant in experimental work. In these cases we consider the loads resistances to be the only resistance. Wiring resistance may be considerable in the case of transmission cables, as well as telephone lines, which are many miles long, and we have a lab which investigates and calculates the resistance in such cables and the lost power and energy due to these lengths. If an arbitrary load of relatively low resistance were connected to an existing power supply or voltage source, an excessive current might flow to the load, causing burn up or other malfunctions with the load and wiring. The current can be reduced by reducing the source voltage, but this is not always feasible and is frequently impossible. The resistances of the voltage source or the load could be increased, but these are usually built right into the source or load. Resistances of connecting wires are so low that miles would be needed to increase the circuit resistance by more than a few dozen ohms. A selection of materials for connecting wires might be useful, but a better method would be to creation of a device that is specifically a resistor that can be included with the circuit to give the net or total resistance needed to provide the desired current for the voltage source involved. In any DC circuit, the total current is equal to the power source voltage divided by the total or equivalent resistance. For a Series Circuit, this is the only current. This means that if the current in some portion of the circuit is known, the total current and the current through every part of the circuit is known. The sum of the voltage drops across the resistors in series is equal to the power supply voltage. In Parallel Circuits, the total current from the power source divides into different paths as in approaches the parallel branches. The voltage drop across parallel branches is the same for all the branches. If the voltage drop for one branch is known, the voltage drop for all the parallel branches is known. The sum of the currents in the various branches is equal to the current from the po.

1. Lab 5: BASIC CIRCUITS
( Resistors, Voltage,
and Current with MATLAB adapted from P-178 DC Circuit
Labs )
Introduction
:
Electric circuits can be defined as closed or continuous paths in
which electric currents are confined and around which electric
currents can be caused to flow. Electrical circuits are an
essential part of daily living, and may be found in heavy and
light industry, commercial installations and operations, and
residential applications. Modern life and its many conveniences
seem inconceivable without the use of electric circuits.
The total resistance of a circuit is the sum of the individual
resistances of the power source, the wiring, and the load. The
load resistance is generally much higher than either the
resistance of the power source or the wiring. The resistances of
the wiring are usually neglected in classroom laboratory
experiments. Very rarely is circuit wiring significant in
experimental work. In these cases we consider the loads
resistances to be the only resistance. Wiring resistance may be
considerable in the case of transmission cables, as well as
telephone lines, which are many miles long, and we have a lab
which investigates and calculates the resistance in such cables
and the lost power and energy due to these lengths.

2. If an arbitrary load of relatively low resistance were connected
to an existing power supply or voltage source, an excessive
current might flow to the load, causing burn up or other
malfunctions with the load and wiring.
The current can be reduced
by reducing the source voltage, but this is not always feasible
and is frequently impossible. The resistances of the voltage
source or the load could be increased, but these are usually built
right into the source or load. Resistances of connecting wires
are so low that miles would be needed to increase the circuit
resistance by more than a few dozen ohms. A selection of
materials for connecting wires might be useful, but a better
method would be to creation of a device that is specifically a
resistor that can be included with the circuit to give the net or
total resistance needed to provide the desired current for the
voltage source involved.
In any DC circuit, the total current is equal to the power source
voltage divided by the total or equivalent resistance. For a
Series Circuit, this is the only current. This means that if the
current in some portion of the circuit is known, the total current
and the current through every part of the circuit is known. The
sum of the voltage drops across the resistors in series is equal to
the power supply voltage.
In Parallel Circuits, the total current from the power source
divides into different paths as in approaches the parallel
branches. The voltage drop across parallel branches is the same
for all the branches. If the voltage drop for one branch is
known, the voltage drop for all the parallel branches is known.
The sum of the currents in the various branches is equal to the
current from the power supply.
Circuits with combinations of Series and Parallel portions or

3. sections are more complex. The current through different
sections is not the same and the voltage drop across various
branches is not the same either.
Ohm’s law is the relationship between voltage, current, and
resistance, and is used to calculate current, voltages, or
resistances in relatively simple circuits that may be reduced to a
simple circuit consisting on one voltage source and on
resistance. For more complex circuits, including series and
parallel portions and branches that might not be reducible or
readily reducible to a single resistor, the application of
Kirchhoff’s Rules is used to solve for various branch currents,
branch voltages, total current and power.
Kirchhoff’s Rules are two, the Junction Rule and the Loop Rule.
The Junction Rule says that the sum of currents entering a node
must equal the sum of currents leaving the node. The Loop Rule
says that the sum of the voltage sources around a loop must
equal the sum of the voltage drops or i*R drops around the same
loop. Algebraically these would be:
Σ
i = 0.0
(Node Rule)
and
Σ
V

4. =
Σ
i*R
or
Σ V
–
Σ i*R = 0.0
(Loop Rule)
Various sections are from Total Circuit Resistance:
Mileaf, 7
th
ed pages 2-20, 2-22, 2-106
Equipment for each Group:
PASCO Electronics Kit.
Large Power Supply.
Multimeter.
Additional connecting wiring as needed.

5. Procedure
:
From the PASCO Electronics Kit select 5 resistors with values
approximately equal to those tabulated here:
Number of Resistor
1
2
3
4
5
Resistance (ohms)
98.
330.
550.
995.

6. 33.
Task 1
.
a. (5) Measure and Tabulate the values of the Resistors in the
Data Sheet provided.
b.
Place the Resistors in the arrangement shown in the Lecture
Notes of Lect_Circuits.
Note there are no resistors in Series or in Parallel. The circuit is
irreducible.
c.
Connect the Power Supply and set it to 15.0 volts.
d. ( 5) Measure and record the Voltages across each resistor in
the Data Sheet provided.
e. (10) Calculate and record the Currents through each Resistor
using Ohm’s Law.
Task 2
.
During today’s Lab Session complete these steps f – i :
f.

7. ( 6)
Write the Kirchhoff’s Node Rule for nodes
b
and
c
;
g.
(12)
Write the Kirchhoff’s Loop Rule for loops I, II, and III.
h.
( 5)
Substitute the values of the Power Supply and the five Resistors
into the equations.
i.
( 5)
Arrange the five equations in Matrix Format as preparation for
entry into MATLAB.
Task 3
.
When you have access to MATLAB complete the following
steps j – l :

8. j. (15)
Solve the five simultaneous equations for the five currents using
MATLAB and tabulate the values of current in the
Data Sheet below the measured values. Print out the MATLAB
script file or workspace and results.
k. ( 5)
Calculate and tabulate the Percent Differences between the
measured values of current and the ‘Theoretical’ values
of current from MATLAB; use the MATLAB values as the
denominator.
l.
( 5)
Calculate and record the Equivalent Resistance of the circuit
using the measurements and again using the
MATLAB results.
m. (1)
Think about how you would calculate and fill in the various
‘Total’ entries in the Data Sheet, and fill them in.
Deliverables and Typed Memo Write-Up from Each Student

9. :
1. (5) Brief Introduction discussing the importance of Circuits
and Ohm’s law. Do not simply copy the material I sent.
2.
Neatly completed Data sheet and a paper copy of the MATLAB
script file used to calculate the currents.
Equations for Kirchhoff’s Node Rule for nodes
b
and
c
;
Equations for Kirchhoff’s Loop Rule for loops I, II, and III.
The equations with values of Resistors and Power Supply
substituted
into the equations.
The five equations written in Matrix Format as preparation for
entry into MATLAB.

10. 3. Discussion Questions,
Conclusions,
a. (2)
Which set of values of current do you believe to be the more
accurate?
b. (2)
Which measurements contributed to the uncertainty of obtaining
the currents from Task 1?
c. (2) Which measurements contributed to the uncertainty of
obtaining the currents from Task 3?
d. R
1
and R
2
appear to be in parallel; are they?
How do you know:
i. )
(3)
Experimentally

11. ii )
(3) Theoretically
e. R
3
and R
5
appear to be in series; are they?
How do you know:
i. )
(3) Experimentally
ii )
(3) Theoretically
4. Conclusions
a. (3) What did you learn from this lab?
b. Suggested recommendations for improvements, if any.
I will post the data sheet when the deal is done