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EXPERIMENT 4
PHYSICS 250
DC ELECTRICAL MEASUREMENTS
Apparatus:
Regulated power supply
Signal generator
Electronic multimeter
DC voltmeter
DC milliammeter
Resistors
Photocell
Dry Cell
Introduction
In modern experimental laboratories associated with the physical sciences, most
measurements are electrical in nature and involve the detection of either voltage or current. Numerous
devices have been developed that will transfer physically meaningful information such as magnetic
field, temperature, light intensity, etc. into electrical voltages or currents so that these physical
quantities can be quantitatively determined by using electrical measurement techniques. Examples of
such devices, known collectively as transducers, are microphones, photocells, temperature sensors,
magnetometers, pressure sensors, etc.
In this experiment you will learn some basic principles relating to the limitations of any such
voltage or current source. You will also study the characteristics and limitations of standard electrical
meters that are used to make the voltage and current measurements. All pieces of scientific equipment
such as meters or voltage sources are designed to perform specific functions to meet ideal
expectations as well as possible. Since each piece of equipment is made of physical materials, it
exhibits limitations, especially when used under conditions not specifically considered during the
design. You can obtain meaningful measurements with such equipment only if you understand these
limitations.
Your laboratory experience this week will be enhanced if you will spend fifteen minutes
reviewing the section of your physics textbook that discusses simple DC circuits. This section
includes Ohm's law (V = IR), Kirchoff's laws ( V = IR = 0 around a closed loop, I = 0 into a
node), and the rules for combining resistances in parallel and in series.
A. Voltage Sources
An ideal voltage source (Emf) would supply a constant output voltage independent of what
is connected to the output terminals. Such is generally not the case for real sources since most voltage
sources, batteries, photocells, and signal generators, for example, have an internal resistance, as
illustrated in Fig. 1. If a small resistance, r, is attached to the output of the voltage source a large
current flows and the output voltage across the terminals of the source decreases due to the Ir voltage
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drop across the internal resistance. Thus the output voltage V0 is
V 0 = Emf - Ir.
(1)
The value of r may be small for some batteries but quite large for photocells, thermocouples, signal
generators, and other physical sources of Emf. If a
resistance approximately the size of r or smaller is
placed externally across the output of the voltage
source, VO will drop significantly due to the current
through r. Expensive regulated voltage sources have
electronic circuits that automatically compensate for
any decrease in the output voltage by increasing the
internal Emf and thus have a very small effective r.
Even regulated voltage sources can supply only a
limited amount of current and will fail to regulate if the
external resistance is too small.
You can consider some transducers and some
electrical sources to be current sources rather than
voltage sources. Specifically, there are available Figure 1. Internal resistance of a voltage
electronic current-regulated sources that electronically source.
maintain the current at some output value rather than
regulate the voltage. Some transducers fit the concept of a current source in that the current is more
closely related to the physical quantity being detected. Fig. 1 is not applicable to this type of device.
B. Electrical Meters
As a scientist you would like to have an ideal electrical voltmeter that would measure all
voltages from microvolts to megavolts and an ideal ammeter that would measure from one
nanoampere to hundreds of amperes with great precision and reliability independent of the
characteristics of the circuit within which you use the meter. Meters that operate in such an ideal way
are not possible. When you use a real meter, you must take care in interpreting the readings because
the insertion of the meter into a circuit changes the circuit since some current must pass through the
meter or some voltage is required to activate the meter.
The electrical meters commonly used in scientific work are based on two-fundamental
devices: (1) the d'Arsonval movement which is essentially a passive current-measuring device, and
(2) the electronic comparator, which is an active voltage-measuring device that requires an internal
voltage source. Either device can serve as the essential element of both a voltmeter and an ammeter
if you attach appropriate resistors, as discussed in detail below. The d'Arsonval movement was
developed over one hundred years ago and was the heart of all electrical instruments prior to the mid
nineteen seventies. It is still used in many of the less expensive instruments of today.
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The d'Arsonval movement consists of a coil of
wire placed in a magnetic field and attached to a
torsional spring. If an electrical current passes through
the coil, a torque is produced by the magnetic
interaction, and the coil rotates against the spring,
which resists with its own torque that is proportional
to the rotation. A needle is attached to the coil to
measure the rotation angle, which is proportional to
the electrical current. This meter movement is
basically a current meter, and by its construction it has
an internal resistance associated with the wire of which
the coil is made. The top portion of Fig. 2 shows a
d'Arsonval movement as an ideal ammeter A with an
internal resistance r.
Figure 2. Details of a d'Arsonval ammeter.
If you are to measure a very small electrical
current, the coil of the movement must have a very
large number of turns to increase the total torque, but more turns will increase the internal resistance.
This situation is undesirable but unavoidable. Internal resistances of 100
or larger are not
uncommon for highly sensitive d'Arsonval movements.
It is rather simple to increase the range of
measurable currents for a d'Arsonval meter. If a
resistance of precisely the value of r/9 is placed in
parallel with the movement, as illustrated in Fig. 2,
only one-tenth of the current I entering at point (a)
will pass through the movement while nine-tenths
of I will go through the by-pass resistor. The
movement with the by-pass resistor inserted will
deflect to full scale when ten times as much
current flows into the circuit as when no by-pass
resistance is used.
Figure 3. Details of a d'Arsonval voltmeter.
It is also rather easy to make the
d'Arsonval meter operate as a voltmeter. If a large resistance R is placed in series with the meter,
movement as shown in Fig. 3, the voltage across the combination is given by V=(R + r)I and is
proportional to I. Thus, by selecting r carefully, you can create a voltmeter of any desired range by
using a single d'Arsonval meter down to a range V = r Im where Im is the maximum current reading
of the movement.
The electronic comparator is an alternate method of measuring DC electrical currents and
voltages. With electronic amplification, you can detect very small voltage differences and can make
a comparison with a reference voltage with great precision. It is also possible to provide a physically
continuous variation of voltage from zero to Vmax to serve as a variable voltage reference.
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The electronic meter makes a comparison
with a reference voltage of the same size and reads
(usually on a digital display) the reference voltage.
In contrast to the d'Arsonval meter, which is
basically an ammeter, the electronic meter is
basically a voltmeter. The electronic amplifier that
makes the comparison requires very little electrical
current and is thus said to have a very high input
resistance. The meter can be diagramed as shown
in Fig. 4 where V is an ideal voltmeter with infinite
internal resistance and r is very large (usually 10
M ). You can change ranges on an electronic
voltmeter by comparing only a fraction of the
Figure 4. Details of an electronic voltmeter.
voltage across the internal resistance with the
reference voltage as indicated in Fig. 4. This
change in ranges does not alter the input resistance of the meter.
You can make an electronic meter operate
as an ammeter by simply inserting a resistance
across the terminals as shown in Fig. 5. Since R
<< r, the voltage detected by the comparator is
given by V = IR, which implies the reading on the
meter is directly proportional to I. The value of r
then determines the range of the meter. Commonly
found meters will have a maximum reference
voltage of approximately 0.2 volts with
sensitivities down to 0.01 millivolt or less. Note
that when the electronic comparator is used as an
ammeter, there is always a voltage drop of
approximately 0.2 volts across the meter.
Figure 5. Details of an electronic ammeter.
At this point you should note that since an
ammeter is put in or becomes part of a particular wire of the circuit (the current must pass through
the meter), an ideal ammeter would have zero internal resistance. Such an ammeter would have no
voltage drop across it and thus would not change the voltages in the circuit. A voltmeter is put
across a particular portion of the circuit, and an ideal voltmeter would have infinite resistance. Such
a meter would allow no current to pass through it and thus would not influence the circuit.
Unfortunately, we do not have ideal ammeters or ideal voltmeters. When you place a meter
in a circuit, you must remember that you have in fact placed a resistance of some type in the circuit
and thus have changed the circuit, hopefully not too much. The electronic meters are in general much
more ideal than the d'Arsonval meters. Specifically, the electronic meter used as a voltmeter is
excellent, but the electronic meter used as an ammeter still has serious limitations.
Using modern solid-state electronic techniques, you can build a so-called preamp that has an
effective input resistance 1013 or greater. You can use such preamps with an amplification of
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precisely 1.000 (no amplification at all) in conjunction with a voltmeter to isolate the voltmeter from
the circuit and still measure the voltage. This combination represents a very ideal voltmeter. You
will make two simple measurements using this technique.
Objective: To learn the use and basic limitations of
standard electrical voltage or current sources and
simple electrical meters.
Procedure
A. Internal Resistance of the Source of Emf
In order to understand the significance of the
internal resistance for an Emf, you will measure r for
an Emf. To determine r for a specific Emf, place a
resistance R and also a voltmeter across the Emf, E,
as illustrated in Fig. 6. From Kirchoff's loop
theorem, the current flowing through the circuit is i
= E /(r + R), and the voltmeter, which can be
assumed to have a very large internal resistance, will
read
V = E - ir = E -
Figure 6. Study of the internal resistance of a
voltage source.
Er
r
= E 1r+R
R+r
(2)
Note that if R is infinite, V = E, but for smaller R, V is less than E. For example, if r = R, V
= E/2. By using resistances of different values and starting with R large, you can find by trial a
resistance such that V is significantly less than E, for example, V = 0.5E to 0.8E. For such a specific
resistance, the measurement of V and R, along with the measured value of E when R = ∞, yields r
from equation (2).
Study one of the following types of Emf :
1. The simple storage battery
Compare r for a D-cell, a 9-volt transistor battery, and a watch (or computer) battery.
2. Photocell
Compare r for a solar cell and a photographic light intensity meter. Hint: Set each at a
fixed distance from a light bulb.
3. Audio signal generator
Check whether r changes with frequency. Use frequencies above 10 Hz.
B. Use of Electrical Meters
Here are three general comments pertinent to the experimental use of electrical meters:
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1.
When you use a meter with multiple ranges and functions, you should first check and
set the switch position that determines the type of measurement (ohms, volts, amps,
AC, DC and the range) before you connect the meter into the circuit. If you do not
have a good estimate of the required range, start with a large range and after you insert
the meter, move to smaller ranges.
2.
Note which of the two connecting wires to the meter you expect to be positive relative
to the other wire. This determination is particularly important when you use d'Arsonval
meters since if you connect the wires in reverse, the needle moves in the wrong
direction, and you will obtain no reading and can damage the meter.
3.
An ammeter inherently has a small internal resistance and thus must always be
connected in series with a sizable resistance that will limit the current. THIS
PRECAUTION IS CRUCIAL SINCE HIGH CURRENTS WILL DESTROY THE
AMMETER. You should never put an ammeter in parallel with any element; an
ammeter is always placed in series with the element through which the current you wish
to measure is flowing. You should always put a voltmeter in parallel with the element
across which you desire to determine the voltage.
Below is an exercise for measurement of electrical voltages and currents in a circuit that is so
simple that only Ohm's law, V = IR, is required to analyze them. You will see, however, that even
in these simple situations, depending on the resistances involved and the meters used, the meter may
read values different from values you might expect based on circuit theory that neglects the meters.
In each situation, think about the effect of the meter in the circuit and then explain why the meter
reads what it does.
1. A simple resistance measurement
a.
b.
From your set of resistors, select
a resistance between 100 and
1000 . Use the electronic
meter to determine its value;
then put the resistance in each of
the circuits shown in Fig. 7.
Using electronic meters, record
the current and voltage and then,
assuming the meters are ideal,
calculate R from the data
obtained.
Figure 7. Study of the effects of meters in a
simple circuit.
Using two d'Arsonval meters,
repeat (a). Why do you now obtain different values of R? Is either value
correct? Explain the source of error in each case. To answer these questions,
you will want to know the size of the internal resistance for each meter. The
internal resistance for the electronic meter used as a voltmeter is 107 . When
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used as an ammeter, the electronic meter has a voltage drop of approximately
0.2 volts across it. Using one of the electronic meters on the ohm scale,
measure the internal resistances for the different d'Arsonval meters. You may
want to tabulate the values for the several scales you use. Do the values for
different scales make sense in terms of Fig. 2 and Fig. 3 on pages (3) and (4)
above?
c.
If R is very small, which of the two circuits in Fig. 7 gives the best result? If
R is very large (105 to 107 ), which circuit gives the best results? You may
experimentally check this result if you desire.
C. Unknown Emf
Three simple direct measurements of the output of a voltage source illustrate both the output
internal resistance of an Emf and the input internal resistance of a voltmeter or amplifier as outlined
below. Using each of the following three voltmeters, (a) the d'Arsonval voltmeter, (b) the electronic
multimeter, and (c) the electronic meter with a preamp, measure the potential of the unknown source
of Emf provided. This unknown source is actually a dry cell with an artificial internal resistance
inserted. Why is each of these voltage measurements different? Which is correct?
Hint: When measuring the unknown Emf with the preamp, you may find the meter is not completely
stable but jumps around by as much as several hundred microvolts. This erratic behavior is
due to noise pick-up in the connecting wires. If you use short lead wires from the Emf to the
preamp and twist these two wires around each other, and don't move anything including
yourself the noise will be reduced.
Now open the top of the unknown Emf and measure the inserted internal resistance of the
unknown Emf. Knowing the internal resistance of the meters used (107 for the electronic meter
and approximately 1013
for the preamp), calculate what you would expect the voltage
measurements to be and compare the values with your actual measurements.
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