MEASUREMENTS IN RESISTIVE NETWORKS AND CIRCUIT LAWS
LABORATORY
The objective of this experiment is to provide working knowledge of the ammeter, voltmeter,
and ohmmeter as well as their limitations in making measurements in resistive networks. In
addition to the above, verification of Ohm's Law, Kirchhoff's Voltage and Current Laws, as
well an introduction the potentiometer and current and voltage division
will be presented.
A voltmeter is used for measuring voltages. For the measurement of a voltage across a circuit
component, a voltmeter must be connected in parallel with the component so that the voltage
across the voltmeter is the same as that across the component. An oscilloscope is a special
type of voltmeter. (The operation of an oscilloscope is presented in Laboratory 6.)
An ammeter is used for measuring currents. For the measurement of a current flowing through
a circuit component, an ammeter is connected in series with the component so that the current
flowing through the ammeter is the same as that flowing through the component. In other words,
the branch must be disconnected, the ammeter inserted, and the branch reconnected.
An ohmmeter is used for measuring resistances of resistors. If a resistor is in a circuit, one end
of the resistor must be disconnected from the circuit before a resistance measurement is made.
Then, the ohmmeter leads are connected to the resistor terminals. Never connect an ohmmeter
to an energized circuit because the reading will be incorrect.
In measuring a voltage or a current, always start at a high range setting and work down to a
suitable range. This safety precaution will prevent the meter from being destroyed by an
unexpected high voltage or current.
Also, when connecting a meter to a circuit, always consider the effect of the meter on the circuit.
Clearly, a meter should not significantly affect the circuit operation. Otherwise, the presence of
the meter will change the electrical quantity being measured, and thus have an erroneous reading.
Ideally, a voltmeter or an oscilloscope should have an infinite input resistance, and an ammeter
should have a zero internal resistance. Since such meters do not exist, the effect of inserting a
meter should always be accounted for by considering the meter resistance as a part of the circuit.
Consider the circuit shown in Fig. 2.1 in which a voltmeter with input resistance Rv is connected
to measure the voltage across resistor R2 . Ideally, the reading of the voltmeter should be, by
voltage division,
Vs
R2
(R1 + R2 )
The actual reading, however, will be
Vs
(R 2 || R V )
(R1 + R 2 || R V )
where R2 || Rv designates the resistance of the parallel combination of R2 and Rv . Since
R 2 || R v =
R vR 2
(R v + R 2 )
As the resistance Rv approaches infinity, the voltmeter reading approaches the correct value.
Thus, it is desirable for the voltmeter input resistance to be much greater than the resistance of
the resistor that the voltmeter is connected across. Then, the voltmeter will not “load”the circuit.
Figure 2.1
Now consider the circuit shown in Fig. 2.2 in which an ammeter with internal resistance
RA is connected to measure the current flowing in resistor RL. The current, I, that the ammeter
will measure is
I=
VS
( RA + RL )
instead of the correct value of
I=
VS
RL
Clearly, though, the ammeter reading will approach the correct value as RA approaches zero.
Thus, the internal resistance of an ammeter should be negligible in comparison with the
resistances of the resistors that it is in series with.
Fig. 2.2
As mentioned, an analysis should be made of the “new”circuit consisting of the circuit
under test plus the resistance of the meter. Often, this analysis will show that the meter has a
negligible effect on the circuit operation. Then, the meter resistance can be ignored. This is the
desired condition, but one which should be assumed only after careful consideration.
Ohm’s Law
Procedure:
1.
Construct the circuit of Fig. 2.3, using for R a resistor of unknown
resistance obtained from the laboratory TA. Connect an ammeter to measure the
current through R and a voltmeter to measure the voltage across R. Remember to
connect the ammeter in series and the voltmeter in parallel. Also, be sure to use the DC
scales on the meters. Vs is a variable source of voltage.
Fig. 2.3
2.
Vary Vs from -10 V to +10 V in steps of 5 V and measure the current through R and
the voltage across R. Please be aware that the ELVIS station has two different variable
DC outputs, one with a range of 0-12V the other with a range of -12-0V. BE SURE
THAT YOU SELECT THE CORRECT OUTPUT AND CHECK YOUR
CONNECTIONS BEFORE APPLYING POWER.
3.
Plot these results using the horizontal axis for the current, I, and the vertical axis for the
voltage, V. From the plot determine the unknown resistance. Does the plot go through
the origin? Should it?
4.
Check the resistance using the digital ohmmeter.
5.
Insert a DC voltage source of 2V in series with R, as shown in Fig. 2.4.
Fig. 2.4
Now place the voltmeter across both R and the 2V source. Repeat steps 2 and 3 (i.e. do steps
2 and 3 but this time you will measure the current through R and the 2V source and the voltage
across R AND the 2V source).
Comment on the meaning of the term “resistance”by comparing the two graphs.
Prelab:
Consider the circuit of Figure 2.5. Let Vs = 12V.
1.
Find the equivalent resistance seen by the source.
2.
How much current is provided by the source?
3.
Find the current in the 3.3 kΩ resistor.
Kirchhoff’s Voltage and Current Laws
Procedure:
1.
Build the circuit shown in Fig. 2.5.
Fig. 2.5
2.
Adjust the source voltage such that Vs = 12V. Then, measure the voltage across each
resistor and the current in each branch.
3.
Using the data collected in step 2, verify Kirchhoff’s voltage law (KVL) and
Kirchhoff’s current law (KCL).
4.
Using the pertinent results from step 2, experimentally determine the total resistance by
measuring Vs and I, or with the help of Ohm’s law. Compare this with the calculated
resistance.
Potentiometer
A potentiometer (or “pot”) is a circuit component with three terminals as shown in Fig. 2.6.
Terminal 3 is connected to a movable contact or arm. The resistance between terminals 1 and
2 is fixed and is equal to the rated value for the potentiometer. The resistance between
terminals 3 and 1 or between 3 and 2 can be varied by moving the arm up or down. If
terminals 1 and 2 are connected across a voltage source, then the voltage between terminals 3
and 1 and between 3 and 2 can be varied by moving the arm.
Fig. 2.6
Procedure:
1.
Measure the resistance between terminals 1 and 2 of the potentiometer at the lab
station. Then, construct the circuit shown in Fig. 2.7 for Vs = 7 V.
Fig. 2.7
2.
Adjust the potentiometer arm to yield output voltages of Vo = 3 V and Vo = 5 V.
Measure the resistance between points 1-3 and 2–3 for each case. Compile the data
and place in a table.
3.
Show how the results agree with voltage division.