INDIANA UNIVERSITY, DEPT. OF PHYSICS, P400/540 LABORATORY
FALL 2008
Laboratory #1: DC Circuits, Electrical Measurements, and V vs. I
Goal: Measure electrical quantities, verify Ohm's law, investigate the properties
of electrical meters, batteries; explore a voltage divider, measure non-linear V vs. I
characteristics. Particularly for those who have had electronics courses or other labs
before, this lab may seem fairly mundane. To those new to electronics, it serves as an
introduction to the equipment, and to those who are more experienced, an introduction to
different equipment.
1. Ohm's Law
Start off with a very basic circuit, i.e., verify that a resistor obeys Ohm's law, by
measuring voltage V and current I for a few voltages. Construct the circuit shown below
using the variable +V power supply on the breadboard (yellow socket, controlled by the
"+V" potentiometer). Use a digital multimeter (DMM) as a voltmeter (probes in "COM"
and "V" ports) and another as an ammeter (probes in "COM" and low-current port).
Remember that voltages are measured across points in the circuit, while currents are
measured through a part of a circuit. Therefore you usually have to break the circuit to
measure a current.
Variable +
Power
Supply
1.3-15 V −
A
V
20k
Use digital multimeters (DMM's) for both
voltmeter and ammeter
Measure a few values of V and I for two 10-kΩ resistors (from here on, we will
refer to this as a "10k resistor", dropping the symbol for "ohms" as understood) in series
(for a total of 20k). Repeat for a single 10k resistor. Sketch the two "curves" on a plot of
V vs. I. It will be trivial, but it will be an apt comparison to later devices that do not obey
Ohm's Law.
Questions:
The voltmeter is not measuring the voltage at the place you want, namely across
the resistor. Does that matter? How can you fix the circuit so the voltmeter measures
what you want? When you've done that, what about the accuracy of the current
measurement? Can you summarize by saying what an ideal voltmeter (or ammeter)
should do to the circuit under test. What does that say about its "internal resistance"?
Which of the two alternative hookups of the voltmeter is preferable, and why?
Would you have reached the same conclusion if the resistance had been 20 MΩ?
2. Battery: example of a real voltage source
A battery is a voltage source, or a device that produces a voltage difference VS
between its poles. Let us connect a "load" resistor RL between these poles. The smaller
the resistor, the more current flows. As we lower this resistor, eventually the chemical
reaction inside the battery cannot keep up with the demand and the voltage V across the
battery drops, or V < VS. This behavior is as if there is an "output" resistance RS inside
the battery that limits the current flow. Such a "real" battery is shown in Fig. 2.
Fig. 3
Fig. 2
RS
VS
A
RS
+
VS
RL
+
V
Replace the breadboard power supply with a simple 1.5 V battery. To measure
RS, connect a variable load (resistor bank) and a voltmeter across the battery as shown
in Fig. 3. Start at a large load (kΩ) and work your way until I has become a few mA.
Continue until you draw about 100 mA. Be aware that a small RL means a large current,
which alters the battery irreversibly. Be reluctant to apply small loads, and if you do, only
for the duration of the reading.
Make a graph of the measured voltage versus the current. From what you know
of loop laws, etc., express current I in terms of voltage drop (V−VS) and RS. You can find
the constant VS by simply having an infinite resistance load (open circuit). See if your
expression explains your data. Deduce the value of the output resistance RS of your
battery (hint: plot I vs. voltage drop (V−VS)).
3. Incandescent lamp: non-Ohmic
Restore using the variable +V power supply on the breadboard. Turn it down to
its minimum value, i.e., ~1.3 V. Now perform the same measurement of V vs. I for the
small incandescent lamp provided. Increase the voltage across the bulb in increments,
but do not exceed ~4.0 V (it is a flashlight bulb, rated for 3.0 VDC). Also plot your results
on the graph you used to show the resistor's behavior. Get enough points to show how
the lamp diverges from resistor-like behavior.
What is the "resistance" of the lamp? Is this a reasonable question? If the lamp's
filament is made of a material fundamentally like the material used in the resistors you
tested earlier, what accounts for the funny shape of the lamp's V vs. I curve?
4. The Diode
Here is another device that does not obey Ohm's Law: the diode. We don't have
to understand how the diode works yet; it is just an example of a device with a very nonlinear behavior that will prove to be very useful in circuits that we will examine in a later
lab.
We need to modify the test setup here, because you normally cannot just stick a
voltage across a diode, as you did for the resistor and lamp. You'll see why after you've
measured the diode's V vs. I. Do that by wiring up the circuit below.
1k
+5 V
R
A
IN3866
Diode
Polarity
V
Gnd.
In this circuit, you are applying a current and noting the diode voltage that results.
Earlier, you applied a voltage and read the resulting current. The 1k resistor limits the
current to safe values. Vary R (use the 10k potentiometer or "pot" on the breadboard),
the resistor substitution box, and/or in a combination of various fixed resistors, and
examine the I vs. V behavior. Plot it using on a linear plot, and then on semi-log graph
paper.
First get an impression of the shape of the linear plot; just four or five points
should define the shape of the curve. Then draw the same points on the semi-log plot
that compresses one of the axes. (Evidently, it is the fast-growing current axis (vertical)
that needs compressing in this case).
See what happens when you reverse the direction of the diode. Here, you can
vary the voltage ("reverse voltage" in this case) all the way up to its maximum value in
increments and record the current. Also plot this V vs. I curve. I choose a beefy diode.
Many smaller "signal diodes" would quickly fry if you exceeded a reverse voltage of
~5 V.