Download Experiment 1: Measurement and Calculations of Basic Electrical

Experiment 1: Measurement and Calculations of Basic Electrical Quantities
OBJECTIVES
1) To learn how to make basic electrical measurements of current, voltage, and
resistance using multimeters.
2) To study the relationship of Ohm's Law.
3) To learn the various methods of calculating power.
4) To study the accuracy of electrical measuring insturments.
BACKGROUND & THEORY
Definitions for various electrical quantities is as follows:
a) Electric current ( or ) is the flow of electric charge from one point to another, and it is
defined as the rate of movement of charge past a point along a conduction path through a
circuit, or
. The unit for current is the ampere (A). One ampere = one coulomb per
second .
b) Electric voltage ( or ) is the "potential difference" between two points, and it is defined as
the work, or energy required, to move a charge of one coulomb from one point to another. The
unit for voltage is the volt (V). One volt = one joule per coulomb.
c) Resistance ( ) is the "constant of proportionality" when the voltage across a circuit element
is a linear function of the current through the circuit element, or
. A circuit element
which results in this linear response is called a resistor. The unit for resistance is the Ohm( ).
One Ohm = one volt per ampere. The relationship
is called Ohm's Law.
d) Electric power ( or ) is dissipated in a resistor in the form of heat. The amount of power is
determined by
,
, or
. The latter two equations are derived by using
Ohm’s Law (
) and making substitutions into the first equation. The unit for power is the
watt (W). One watt = one joule per second.
Resistors come in many shapes and sizes, but in this class we will use small carbon film
resistors. Some points to note about carbon film resistors are as follows:
a. The value of resistance is indicated by color coded bands around the body of the resistor.
Figure 1 shows how to read the resistance and tolerance of a four-band resistor.
Figure 1
b. The power rating of the resistor is determined by its physical size while the resistance
value is determined by its internal composition. A resistor which has a larger physical size
has a larger surface area to transfer heat to the surrounding air and therefore can
dissipate a larger power without overheating. Most of the resistors used in our lab
experiments will be ½ W or ¼ W resistors.
c. Typical standard resistor values are 1.0, 1.2, 1.5, 1.8, 2.2, 2.7, 3.3, 3.9, 4.7, 5.6, 6.8, 7.5, 8.2,
and 9.1 multiplied by a power of 10.
Meters are used to make measurements of the various physical variables in an electrical circuit.
These meters may be designed to measure only one variable such as a voltmeter or an
ammeter. Other meters called multimeters are designed to measure several variables, typically
voltage, current and resistance. These multimeters have the capability of measuring a wide
range of values for each of these variables. Some multimeter operate on battery power and are
therefore easily portable, but need battery replacement. Others operate on a.c. power.
The read-out, or display, of value being measured on the multimeter may be of the digital type
or the analog type. The digital type displays the measurement in an easy to read form. The
analog type has a pointer which moves in front of a marked scale and must be read by visually
interpolating between the scale markings.
EQUIPMENT AND PARTS LIST
Digital Multimeter (DMM)
Adjustable DC power supply
Circuit breadboard
Resistors:
,
,
PROCEDURE
1) Note the color code on each resistor and determine its nominal value from the color code
table in Figure 1. The first two color bands give the two significant digits for the value. the next
band tells how many zeros to put after the first two digits. The fourth band tells the tolerance
specification for the resistor value. No fourth band = 20%. Silver = 10%. Gold = 5%.
2) Measure and record the actual value for each resistor. The meter range should be set so that
you obtain the most accurate possible value. There should be at least three significant figures
in each measurement. Make a tabulation showing the marked or nominal value, the measured
value, and the percentage error for each of the resistor. To calculate the percentage error, Use
the following formula:
3) Set the DMM to D.C. voltage. Turn on the D.C. power supply and adjust the power supply to
its lowest value. Then measure and record the power supply output voltage. Then adjust the
power supply for its maximum output value. Measure and record this value. Do this for all the
outputs of the power supply. Note the terminal marked COM is the common reference node
for all three of the outputs. The black terminal marked ground is connected only to the third
prong safety ground of the ac line cord and is not internally connected to any of the three DC
power supplies.
4) Mount the resistor on the circuit breadboard so that the wires from each end of the
resistor are not put in holes which are connected. Then connect the power supply output to the
two ends of the resistor using jumper wires. Your circuit should look like the schematic diagram
shown in Figure 2:
Figure 2
The breadboards have a set of holes spaced 0.1 inches apart and arranged in a pattern similar
to that shown above. At the top and bottom edge of the board are two horizontal lines with
several groups of five holes in each line. All the holes in each of these lines are electrically
connected together as shown by the red and blue lines. In the center section of the board are
two sets of vertical lines with five holes in each line. There is a 0.3 inch space between the top
and bottom set to match the standard spacing of pins on integrated circuit (IC) chips. All the
holes in each group of five are connected as shown by the black lines. There is no connection
across the central channel. the holes will accept the solid wire leads of most electronic
components. Figure 3 shows a
resistor with its leads inserted into the middle holes of
two different lines of five holes.
Figure 3: Breadboard Layout
To connect the DC power supply to the resistor, the common lead from the power supply must
be inserted into one of the other four holes of the line at one end of the resistor and the +V
lead must be inserted into one of the holes of the line at the other end of the resistor.
Figure 4
The common lead of the meter voltmeter should go to the common side of the resistor. The
Volt lead of the meter should go to the other side of the resistor to measure the voltage across
the resistor. Your circuit should look like the schematic diagram shown in Figure 5:
Figure 5
5) In the circuit above, adjust the voltage source, V, to approximately 5.0 V D.C., using the DMM
to measure voltage. You should have at least three significant figures in your measurements.
6) Next break the circuit and insert the DMM to measure and record the current through the
series circuit above right. Keep the setting of the voltage the same as in 6. (Be sure to check the
DMM for proper selection of ranges, variable, and position of the leads). Do you have three
significant figures in your measurement?
Figure 6
The mA meter should be connected between the +V side of the power supply and the side of
the resistor where the power supply lead was previously connected. The meter and its leads
act as the connection from the power supply and the resistor so that all the current flowing
through the resister must flow through the meter to get to the resistor. This allows the meter
to measure the same current that is flowing through the resistor. To get the proper sign for the
current into the positive terminal of the resistor, the positive terminal of the power supply
must be connected to the mA terminal of the meter and the com terminal must be connected
to the resistor. Your circuit should look like the schematic diagram shown in Figure 7:
Figure 7
7) Repeat the procedure in 5 and 6 above with each of the other two resistors.
8) Repeat the procedure in 5, 6, and 7 above for V = 10 V D.C. and V = 15 V D.C.
CALCULATIONS AND GRAPHS
1. Make a graph of current ( axis) versus voltage ( axis) for your 1- resistor. Does the
current increase linearly with the voltage? On the same graph, compare to a theoretical line of
constant R. I recommend using a computer spreadsheet to plot the graphs.
2. Using Ohm's Law, calculate current (I) with a constant voltage of 10 V D.C. for each of the
three nominal resistances (
,
,
). Does the current decrease linearly with
resistance? Make a graph of current ( axis) versus resistance ( axis) to show your calculated
and your measured results. If you use a spreadsheet you can easily calculate extra data points
between the values of the resistances used in the experiment and then plot a much smoother
curve. Try this using steps of 0.1
from 1
to 5 . Plot this theoretical curve with a line
between points and no symbols. Plot the experimental data on the same graph using symbols
but no line.
3. Using the experimental measurements, calculate the power dissipated in each of the three
resistors at each of the three voltages using all three methods,
,
, or
.
4. Make a graph of power ( axis) versus resistance ( axis) using your calculated results from
step 4 above. Does the power decrease linearly with resistance?