EE 442 Laboratory Experiment 2
Introduction to the Measurement of Voltage, Current, Resistance; and Voltmeter Loading
EE 442
Lab Experiment No. 2
1/17/2007
Introduction to the Measurement of
Voltage, Current, Resistance; and
Voltmeter Loading
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EE 442 Laboratory Experiment 2
Introduction to the Measurement of Voltage, Current, Resistance; and Voltmeter Loading
I.
INTRODUCTION
The purpose of this experiment is to become familiar with a multimeter
and to use it to make voltage, current, and resistance measurements. A
final aspect of this lab is to understand how a piece of test equipment
affects the circuit it is connected to.
II.
PRELIMINARY BACKGROUND READING
A. INSTRUMENT DESCRIPTION
General Remarks
All voltmeters, ammeters, and ohmmeters make measurements by
means of a two terminal connection to a circuit or circuit element
under test. All voltmeters, ammeters, and ohmmeters have at least two
jacks into which only two test probes are inserted. If there are more
than two jacks on the face of a particular meter, there is usually an
indication of some sort, next to each jack, to inform the user which
jacks to use to measure a particular quantity.
Many times a voltmeter, an ammeter, and an ohmmeter are combined
into one package called a multimeter. Multimeters come in two
flavors: analog and digital. Analog meters have a display that consists
of a needle which points to a number scale. These meters have
function and range controls which allow the user to select what kind of
meter (voltmeter, ammeter, or ohmmeter) the multimeter will be and
what range of values the meter will read. Digital multimeters typically
have a LCD or LED display and in many cases are auto-ranging. That
is, the meter will automatically select the most appropriate range for
making the measurement. In this lab either an analog or a digital
meter can be used with little difference in operation.
Voltmeter
A voltmeter measures electrical potential between its terminals.
Voltmeters are always placed in parallel with the circuit or circuit
element where the voltage measurement is desired. Since the voltage
across two or more parallel elements is the same, the voltage measured
by the meter will be the same as the element to which the meter is
connected. When using a non-auto-ranging meter, select the highest
possible range and reduce the range as necessary until the desired level
of accuracy is reached. Always start with a range higher than the
expected
value
to
prevent
damage
to
the
meter.
Ammeter
An ammeter measures the current that flows between its terminals. An
ammeter is always placed in series with the circuit or circuit element
where the current flow is of interest. Since the current in each element
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EE 442 Laboratory Experiment 2
Introduction to the Measurement of Voltage, Current, Resistance; and Voltmeter Loading
of a series circuit is the same, the current flow through the meter will
be the same as the current flow to the element of interest. Never
connect an ammeter in parallel unless you intend to measure
the short circuit current of a circuit or circuit element and
you have made sure that destructive current levels won’t be
reached. When using a non-auto-ranging meter, select the highest
possible range and reduce the range as necessary until the desired level
of accuracy is reached. Always start with a range higher than the
expected value to prevent damage to the meter.
Ohmmeter
An ohmmeter measures the electrical resistance between its terminals.
An ohmmeter is connected to the circuit or circuit element of interest
after the element of interest has been isolated from the rest of the
circuit. The element of interest has to be isolated from the rest of the
circuit so that its resistance value isn’t obscured by the resistance
values of the other circuit components connected to the element of
interest. Never connect an ohmmeter to an energized circuit
or the meter could be destroyed. There is an additional caveat for
an analog ohmmeter; it has to be zeroed every time the resistance
range is changed. To zero the analog ohmmeter, touch its probes
together (the needle will deflect to approximately full scale, use the
“zeroing” knob to adjust the needle to read zero. The analog meter can
now be used in this particular range.
Zeroing Needle-Indicating Meters
Before meters with mechanical needle displays can used the displays
need to be zeroed. This procedure is performed with the piece of
equipment turned off and the equipment placed in the position where
it will be used. Use a screw driver to turn the adjusting screw near the
base of the needle until the needle is on the zero mark.
Precautions
1.
Never leave a multimeter on any ohms scale. If the
meter must left on, set it to its highest DC voltage range.
2.
Never make a resistance measurement on a circuit element
while the circuit is energized.
3.
Always turn test equipment off (if possible) when it is not in
use.
4.
Never connect any meter to any circuit before
adjusting the function and range controls
appropriately.
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EE 442 Laboratory Experiment 2
Introduction to the Measurement of Voltage, Current, Resistance; and Voltmeter Loading
B. METER LOADING
Discussion
Ideally, a meter would have no effect on the circuit that it is measuring.
In reality, however, it is not possible to make a measurement without
having some effect on what is being measured. These effects can
usually be ignored, but a good engineer will make sure that assuming
the meter to be ideal is a valid assumption.
Since a voltmeter is connected in parallel to a circuit or circuit element
being measured, it should ideally have an infinitely high resistance.
This condition is necessary so the parallel combination of the meter
and the circuit element do not result in a different total impedance
than what the circuit element originally had.
Since an ammeter is connected in series with a circuit or circuit
element were the current is of interest, it should have no resistance and
resemble a short. As a short, the ammeter would have no effect on the
total impedance of the circuit or circuit element being measured. It
should be obvious now why an ammeter shouldn’t be connected in
parallel to the circuit or circuit element of interest. The ammeter is a
short circuit which could draw excessive currents.
In reality, neither voltmeters nor ammeters have ideal resistances. A
typical voltmeter will have a resistance on the order of a million to
several million ohms. A typical ammeter will have a resistance on the
order of tenths to hundredths of an ohm. When performing circuit
analysis, the meter should be replaced with its approximate resistance.
In this manner, the non-idealities can be accounted for. If a voltmeter
is placed in parallel with a circuit or circuit element and the difference
between the resistance of the circuit or circuit element and the
resistance of that circuit or circuit element parallel combined with the
resistance of the meter are insignificant, then the effects of the meter
can be neglected. A similar statement can be made for the ohmmeter.
Example
As an example of voltmeter loading, consider the following circuit
(Figure 1) where voltage measurement across the 30 kΩ resistor is
desired.
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EE 442 Laboratory Experiment 2
Introduction to the Measurement of Voltage, Current, Resistance; and Voltmeter Loading
R1
10k
R2
20k
V1
120Vdc
A
+
R3
30k
VAB
B
0
Figure 1 Series circuit
Preliminary calculations suggest that the voltage from points A to B
will be 60V. Assume a voltmeter with an internal resistance of 60
kΩ is connected across terminals A and B (Figure 2).
R1
10k
R2
20k
V1
120Vdc
A
+
R3
30k
RM
VAB
60k
B
0
Figure 2 Series circuit being loaded by a voltmeter
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Voltmeter
EE 442 Laboratory Experiment 2
Introduction to the Measurement of Voltage, Current, Resistance; and Voltmeter Loading
It can easily be determined, as shown below, that the new
resistance between terminals A and B has decreased to 20 kΩ.
REq =
R M R3
60kΩ ⋅ 30 kΩ
=
= 20kΩ
R M + R3 60 kΩ + 30 kΩ
The difference between the resistance of the branch without the
meter and the resistance of the branch with the meter is 10 kΩ
which is certainly significant. Using the voltage divider formula, we
can see that the meter reads a significantly different voltage than
what was expected through preliminary calculations.
20 kΩ
⎛
⎞
v AB = ⎜
⎟120 = 48
⎝ 10 kΩ + 20 kΩ + 20 kΩ ⎠
Note the VAB would change if any finite resistance were connected
across terminals A and B. Voltmeter loading always occurs and is
simply a matter of degree.
C. RESISTOR COLOR CODES
The values of most of the resistors in you lab kit are indicated by color
bands. These color bands are painted on the body of each resistor and are
decoded in the following manner:
Look at the resistor. There will be a group of color bands clumped together
at one end and a lone band at the other. Orient the resistor so the lone
band points to the right and the clumped bands point to the left. The
resistor can be read left to right using the guidelines listed below.
1. The first color band indicates the first digit in the numerical
value of the resistance.
2. The second color band gives the second digit in the numerical
value of the resistance. Any subsequent bands before the last
band in the “clump” give subsequent digits in the numerical
resistance value.
3. The last color band in the “clump” gives the number of zeros
that follow the first digits.
4. The “lone” color band on the right end gives the tolerance.
Note: Tolerance is the amount by which the actual resistance can be
different from the color-coded value and it is given in percent. For
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EE 442 Laboratory Experiment 2
Introduction to the Measurement of Voltage, Current, Resistance; and Voltmeter Loading
example, a 1000 Ω resistor with a +-10% tolerance can have an actual
resistance value between 900 Ω and 1100 Ω.
The color codes for digits and tolerance are given in Figure 3. Your
instructor might suggest a convenient mnemonic which may help you to
remember the code.
(Image courtesy http://www.elexp.com)
Figure 3 Resistor color codes
III.
PRELAB EXERCISES
A.
Current Calculations
In part D of the lab exercise section (V) of this experiment, current
measurements will be made on a series connected circuit. To
provide a basis for comparison, those currents will be calculated as
a preliminary problem. Calculate the current i for different values
of resistance R (Figure 4) and record below.
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EE 442 Laboratory Experiment 2
Introduction to the Measurement of Voltage, Current, Resistance; and Voltmeter Loading
R1
10k
i
V1
10Vdc
R
0
Figure 4 Circuit for current calculations
B.
R = 0 Ω,
i = _____________.
R = 5 kΩ,
i = _____________.
R = 10 kΩ,
i = _____________.
Voltmeter Loading Calculations
In part E of the lab exercise section, the following circuit (Figure 5)
will be used to investigate voltmeter loading. Calculate VAB and
record below.
R1
100k
A
V2
+
R2
100k
4Vdc
VAB
-
B
0
Figure 5 Voltmeter loading circuit
VAB = ___________________.
The meters will be represented as resistances with the digital
multimeter having a resistance, in its DC mode, of 10 MΩ. The
resistance of the analog multimeter will be 50 kΩ when it is used on
its 2.5 Volt range. The resistance of the digital multimeter is found
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EE 442 Laboratory Experiment 2
Introduction to the Measurement of Voltage, Current, Resistance; and Voltmeter Loading
from its specifications sheet while the resistance of the analog
multimeter is calculated by multiplying its sensitivity (found on its
specifications sheet) by the range it is being used in.
( 20kΩ / V ⋅ 2.5V = 50kΩ )
Calculate the voltages these two meters would read if each were
separately connected to terminals A and B. Record your results
below.
VABDMM = ___________________________.
VABAMM = ___________________________.
Finally, calculate VAB read by each voltmeter if the two 100 kΩ
resistors were replaced by two 1 kΩ.
VABDMM = ___________________________.
VABAMM = ___________________________.
IV.
LABORATORY EXPERIMENTS
In the first three parts of the performance section of this experiment an
analog and a digital multimeter will be used. Compare the readings of
both meters and report any major discrepancies to you lab instructor.
A.
DC Voltage Measurement
Set the DC supply to a voltage of your choosing using the meter on
the face of the supply. Write down this voltage value. Use both an
analog and a digital meter to measure the DC voltage of the supply.
Remember to start in the highest range and work your way down
when using an analog meter. (The most accurate measurement is
made when the needle is in the middle of the scale).
VDCSUPPLY = ___________________.
VDMM = ________________________.
VAMM = ________________________.
B.
AC Voltage Measurement
Set the signal generator to output a sinusoid 10 V p, 10 kHz.
Measure this voltage with the scope, analog multimeter, and digital
multimeter. Note, the multimeters read volts RMS. RMS stands
for root-mean-square which is defined as follows
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EE 442 Laboratory Experiment 2
Introduction to the Measurement of Voltage, Current, Resistance; and Voltmeter Loading
v RMS =
1
T
∫
T
0
v ( t ) 2 dt .
A more formal presentation about RMS will be given later. For
v
now, you just need to know that for a sine wave v RMS = P . Your
2
multimeters should both read about 7.07 V rms.
C.
Resistance Measurement
Choose a 10% (or a 5% tolerance if you don’t have a 10%) tolerance
resistor from your kit. Use the color bands on the resistor body to
determine the nominal resistance for the device. Use both an
analog and a digital multimeter to measure the actual resistance of
the device. Is the measured value within the allotted tolerance?
RNOMINAL = ____________________.
RDMM = ________________________.
RAMM = ________________________.
D.
Current Measurement
Build the following circuit (Figure 6).
R1
RM
10k
Ammeter
i
V1
10Vdc
R
0
Figure 6 Circuit for current measurement
Measure the current with both analog and digital meters. Use the
following resistor values for R: 0 Ω, 5 kΩ, 10 kΩ. (Hint: both
meters can be placed in series with each other and the current
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EE 442 Laboratory Experiment 2
Introduction to the Measurement of Voltage, Current, Resistance; and Voltmeter Loading
through each will be the same.) Remember to start in the highest
current range and work you way down.
E.
R = 0 Ω,
iAMM = _____________. iDMM = _____________.
R = 5 kΩ,
iAMM = _____________. iDMM = _____________.
R = 10 kΩ,
iAMM = _____________. iDMM = _____________.
Voltmeter Loading
Consider the circuit below (Figure 7).
R1
100k
A
V2
+
R2
100k
4Vdc
VAB
-
B
0
Figure 7 Voltmeter loading circuit
Measure the VAB with a digital multimeter and record below.
Compare this result with the preliminary result.
VABDMM = ____________________.
Remove the digital multimeter and replace with an analog meter set
on its 2.5 Volt range. Record VAB below and compare this result
with the preliminary result.
VABAMM = ____________________.
Reconnect the digital multimeter across terminals A and B with the
analog multimeter still connected. Record the reading of the digital
multimeter below. Did the reading of the analog multimeter change
from its previous value? Why? Now disconnect the analog
multimeter and note the reading of the digital multimeter. Why did
this reading change?
VABDMM = _________________________.
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EE 442 Laboratory Experiment 2
Introduction to the Measurement of Voltage, Current, Resistance; and Voltmeter Loading
Swap the 100 kΩ resistors for 1 kΩ resistors and measure VAB with
both meters again, compare these results with you preliminary
values.
VABDMM = _________________________.
VABAMM = _________________________.
Explain why these voltage readings were the same as, or different
from, the readings taken from the circuit composed of 100 kΩ
resistors.
V.
CONCLUSION
You should now be an expert at the using the digital multimeter. You
should also be familiar with the effects of a meter on the circuit it is
measuring. Finally you should be able to use the color bands on a resistor
to determine its value.
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