Download EE110 Lab2 Ohm`s Law and Resistor Combinations

Sonoma State University Department of Engineering Science Spring 2017
EE 110
Introduction to Engineering & Laboratory Experience
Saeid Rahimi, Ph.D.
Lab 2
Ohm's Law, Voltage ad Current Measurement and Resistor
Combinations
1. DC Power Supplies
A power supply is a device that provides the energy required to power up a circuit. In
this section we will experiment with DC (Direct Current) power supplies. Of course, we
can use the Discovery Scope (DS) as a source of power while realizing that the DS itself
is powered by your laptop computer. We will experiment with the AC (Alternating
Current) power supplies or function generators in the future labs. Batteries are the most
common types of DC power supplies. Multimeters are commonly used for measurement
of basic electrical resistance, voltage, and current. Today you will use your own
multimeter for measurement of voltage and current.
Your Discovery Scope can deliver +5V and -5V. First test your DS voltage output with
your multimeter. Draw a diagram in your lab book and illustrate the connection between
your multimeter and the positive 5 V source indicating the ground wires. Repeat the
procedure for the – 5 V source. You will use the DS as a DC power supply at home.
Use the laboratory DC power supply for the rest of this lab.
2. Ohm's Law - A review
Ohm's law states that the voltage drop across a resistor has a linear relationship to the
current flowing through the resistor.
V=RI
Graphically this linear relationship (similar to the familiar y = m x) is represented by a
line when the current through the resistor is plotted against the voltage across it. This
graph is termed I-V characteristic of the device. A linear I-V graph indicates that the
resistance of the device remains constant over a wide range of currents and voltages. For
many electronic devices the resistance is not a constant and varies with the applied
voltage and current. These devices possess non-linear I-V characteristics. However, the
slope of the curve at any given point determines the resistance of the device for that
particular current and voltage.
The figure below illustrates a linear V (volts) vs. I (mA) graph. The units are not shown
on the graph. The slope of the graph indicates the device resistance. The resistance of
the device is determined by calculating the slope: R = ∆V/∆I, which is approximately
1.1 kΩ
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In order to generate the above graph we require a variable DC voltage source. The above
linear curve illustrates that if we desire to measure the current through a resistor, we can
measure the voltage drop across it and then divide that voltage by the resistance of the
resistor to obtain the current. The diagram is a graphical representation of Ohm’s law.
3. Resistor Combinations
It is important to understand the effective resistance of resistors when they are connected in
series and/or in parallel. Your toolbox may include resistors with various resistances. Three
resistors will be of interest in this course: 300 Ω, 1 kΩ, and 10 kΩ potentiometer. Today, we
will combine the 300 Ω and 1 kΩ resistors to make resistor combinations with resistances that
do not exist in your toolbox. Resistance of resistors are almost never exactly equal to the value
indicated by the manufacturer. You will notice that there are several bands printed on each
resistor. One can estimate the value of the resistance of the resistor using the color chart
below.
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In the absence of a multimeter, these charts provide a convenient way to estimate the resistance
of a resistor. However, you should use your multimeters to measure the exact resistance of the
resistors that you intend to use in the circuit.
These resistors can be connected to each other (combined) to practically create any desired
resistance. There are rules governing the combination of the electronic elements. Today we will
examine the series and parallel resistor combinations. Capacitors may also be combined
similarly, but their combination rules are different from resistors. Consider the following resistor
combinations.
A. Series Combinations
The equivalent resistance of this combination is:
Re = R1 + R2 + ...
Clearly in a series combination of resistors the same current goes through all resistors. The
above formula can be easily obtained using Ohm's law. The derivation for the equivalent
resistance of series and parallel combination of resistors can be found on the Internet, or in
any elementary electronic text books.
B. Parallel Combination
The equivalent resistance of the parallel combination is given by
1/Re = 1/R1 + 1/R2 + ...
Sometimes we may need to mix series and parallel resistor combinations to achieve a specific
resistance. For cost reduction, the number of components in the circuit should be minimized. A
mixed series and parallel combination of resistors is shown below.
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Measurement 1
Select two 1 kΩ resistors. Verify the resistance of each resistor using the color chart. Using
the last band of the resistors, indicate their percentage tolerance. Illustrate your method in
your lab book. Next, use your multimeter to measure the resistance of each resistor. Present
the expected values (from the color chart) and the measured values (using multimeter) in a
chart. Are the measured values within the tolerance values of the resistors?
Measurement 2
Combine two or more resistors (series and/or parallel) to create an electrical resistance close to
150 and 800. Describe and justify your method and calculate the expected value of the
resulting resistance. Connect the resistors on your breadboard and use your multimeter to
determine the value of each resistor and apply the series and/or parallel combination of
resistors to determine the expected value of the resulting resistor. Compare the observed value
and the expected value of each resistor combination, and make a note of the % error. Present
your expected values (based on calculation) with measured values (using your multimeters).
Important note: When measuring the resistance of a resistor make sure that it is
disconnected from your circuit or breadboard. You will be measuring the equivalent
resistance of the entire circuit if you attempt to measure the resistance of a resistor while it is
connected to the circuit.
4. Current Measurement
Electric current may be measured by your multimeter and other electronic instruments.
However, in this lab we first measure voltage and then use Ohm's law to determine current:
Measure the voltage drop across a resistor and divide by its resistance!
I = VAB / R1
A
R1
B
4.7kΩ
V1
5V
Measurement 3
Construct the circuit shown above on your breadboard. Use the laboratory power supply to
provide the 5 V voltage to the circuit. Use the resistor bins in the laboratory if you do not have
the resistor values indicated in the circuit diagrams. Be sure to measure the resistances before
inserting the resistor in the circuit. Also, be sure to measure the resistance values before placing
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the resistors back in the resistor bins in the lab. Other students will appreciate the care you
exercise in not placing the resistors in the wrong bins. Measure the voltage VAB across resistor
R1 and use Ohm's law to calculate the current through the resistor.
Note: Try to construct at least one or preferably all of the circuits in Multisim and use the
multimeter within Multisim to find the expected voltage and current values!
Measurement 4
Next, add a second resistor in series with the first. Measure the voltage across each resistor
(VAB, VBC) and calculate the current through R1 and R2. The two current values must be the
same. Explain why! Call this current Imeasured.
A
B
R1
4.7kΩ
R2
1kΩ
V1
5V
C
Calculation: Use the series resistor combination rule and calculate the equivalent resistance Re
of the above series resistor combination. Redraw the circuit in your lab book and replace the two
resistors with the equivalent resistor. Use Ohm's law to calculate the current in the circuit and
name it the expected current Iexp . Calculate the % error between Iexp and Imeas :
% error = {(Iexp- Imeas)/ Iexp}* 100
Measurement 5
Take the previous circuit apart and reconnect the resistors in parallel and apply the voltage as
shown the figure below. Measure the current I1 and I2 through resistors R1 and R2, respectively.
The total current supplied by the power supply is I = I1 + I2. Use the parallel resistor
combination rule and calculate the equivalent resistance (Re) of the two parallel resistors.
I
V1
5V
I1
A
R1
4.7kΩ
R2
1kΩ
I2
B
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Redraw the circuit replacing the two resistors with Re. This diagram will be the same as the
circuit of measurement 4, except you replace R1 with Re. Use Ohm's law to calculate the current
through Re. Call this current Ie (should be the same as I). Calculate the % error between the
measured and the expected values. Note that the current I branches out at point A and a portion
of it flows through R1 and the rest of it goes through R2. The current in these two branches I1
and I2 combine at point B and return to the negative terminal of the battery.
Measurement 6
Next add resistor R3 as shown below and use Ohm's law to obtain I, I1, and I2. First measure the
voltage across each resistor and then calculate the current (I = V/R).
R3
C
2kΩ
A
I
V1
5V
I1
R1
4.7kΩ
R2
1kΩ
I2
B
Note that the current I through R3 branches out into I1 and I2. The current through these branches
add up at point B and return to the negative terminal of the battery.
Calculate the equivalent resistance Re of the above circuit. Redraw the circuit substituting Re for
the three resistors in the circuit. Use Ohm's law to calculate the current in this equivalent circuit.
Measurement 7
In order to visually demonstrate the difference between series and parallel resistor combinations,
consider first the series combination of three resistors and then the parallel combination of the
same three resistors. Three identical LEDs are attached to each resistor so you can visually see
the strength of the current in each resistor through the brightness of the LEDs. Construct each
circuit and observe the LED brightness for each combination and translate that to the current
values in each combination.
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Spring 2017
LED2
LED3
R0
R1
R2
R3
100Ohm_5%
200Ohm_5%
200Ohm_5%
200Ohm_5%
V1
5 V
R0
100Ohm_5%
R1
200Ohm_5%
V1
5 V
LED1
R2
200Ohm_5%
LED2
R3
200Ohm_5%
LED3
7