Download Electricity and Measurement Experiments

Electricity and Measurement
Potential difference and energy, current and charge, resistance - the big concepts underlying the
operation of electric circuits - will be the focus of this segment of practical work. It is crucial that
you develop a sound understanding of these ideas in order that you may design circuits for a
variety of applications. The understanding required is much more than facility in manipulating
Ohm’s Law and the series and parallel resistance relationships. These experiments will be
valuable in helping you improve your skills in the construction and analysis of circuits - careful
measurement techniques will be emphasised. In addition, the experiments should help deepen
your understanding of how circuits function.
We commence with some background information on electrical circuits, and a simple introductory
experiment, Electric Circuits- A Review?, to enhance your understanding of the basics of electrical
circuit operation.
You may be familiar with the initial ideas of measurement in electric circuits - ammeters are
connected in series to measure the rate at which charge passes through an electrical component,
while voltmeters are placed in parallel to track the difference in potential energy per charge
between one side of the component and the other. There is a lot more to it though ...
How do the meters affect the quantities being measured? After all, they provide paths for the
charge and so are themselves part of the electric circuit. You will explore this area in the
experiment The Correct Use of Voltmeters and Ammeters.
Can we design our own measuring instruments? You will think about ways of measuring
resistance in the Investigating Resistance experiment. You will be an instrument designer here.
Throughout these experiments you will develop confidence in your ability to wire up and make
measurements in electrical circuits. At the same time, this practice in constructing and
analysing circuits will improve your understanding of the underlying relationships between
current, voltage and resistance.
EM-2
Background Information
Sources of E.M.F.
In general, a D.C. (direct current) circuit consists of a source of E.M.F. (often a battery or a single
cell) and a closed circuit around which a current can flow. E.M.F. stands for the archaic and
misleading term "electromotive force". The source of E.M.F. is a device which maintains a
potential difference between its terminals, and so provides the energy to maintain a current
around the circuit. The E.M.F. is a measure of the electrical energy supplied to charge which
travels from one terminal to the other. It is measured in joule per coulomb, ie. volt (V).
Sources of E.M.F. may be combined in series to give a voltage output equal to the algebraic sum
of their individual voltages; eg. consider a string of dry cells:
A
B
+
-
C
+
1
-
D
+
2
E
-
+
3
4
cell 1 maintains A at a potential VAB above B
cell 2 maintains B at a potential VBC above C, etc.
Therefore, the potential difference (P.D.) between A and E is:
VA - VE = VAE = VAB + VBC + VCD + VDE.
This is sensible - each cell supplies energy to charge which passes through it, and the energy
provided by the whole string of cells is equal to the sum of these energy contributions.
A battery consists of a number of cells connected in series. The voltage quoted on a battery is its
nominal voltage. The actual E.M.F. could be significantly less, depending on the internal
resistance of the battery which is affected by the battery's age and history. A portion of the
nominal voltage is then “lost” due to the energy dissipated as the charge passes through the
battery itself.
Ohm's Law
When a potential difference, V, is applied across a
conductor (eg. by connecting the ends of the conductor
to the terminals of a battery as shown in the diagram),
charge, flows through the conductor. The rate at which
charge flows past each point in this circuit is the
current, I, measure in coulomb per second, ie. ampere
(A).
+
V
This cause/effect relationship between potential
difference (P.D.) and current for many types of
conductor is described by Ohm's law, I ∝ V. It
therefore follows that V/I is a constant, which is called
the resistance R (ohms). Thus,
R = V/I
or
V = IR
R
-
I
or
I = V / R.
EM-3
I (in amps) is the current in a conductor of resistance R (in ohms) when a P.D. of V (in volts) is
maintained between its ends. It is an experimental fact that the resistance R of many
conductors remains essentially constant as the current is varied, and this will be assumed
throughout the following experiments unless stated otherwise. There are some common
exceptions to this sort of behaviour however - the resistance of the fine wire in light globes
increases with temperature, and semiconductor materials experience a decrease of resistance
with temperature and often when exposed to light.
Notes on Wiring Up Electrical Circuits
1.
Before starting to wire up, draw the circuit diagram in your practical book, showing all the
components you are actually going to use. You should always label (i) all components with
suitable symbols or values, and (ii) the positive terminal of every meter with a + sign.
Remember to show the direction of current flow.
2.
It is helpful to arrange the major components of your circuit in the same relative positions
as those they occupy in your circuit diagram.
3.
In connecting up:
(i)
V
If the circuit contains more than one loop, wire up one loop at a time. ie. first wire
one loop completely from one terminal of the input voltage to the other, then wire up
the second loop between the two points where it meets the first, and so on.
+
V
+
V
-
-
+
-
Which is of
course
equivalent to ...
V
+
-
(ii)
When including meters, place ammeters in the circuit when you wire up the loop
containing the component of interest, but place voltmeters in the circuit after all
components have been wired into the circuit.
(iii)
It is often useful to include a switch in order that the battery not be drained
unnecessarily.
(iv)
Connect the battery last.
(v)
When you do finally connect the battery, momentarily touch the terminal with the
lead, check that all meters turn the right way and that they are not overloaded.
Make sure every member of your group gains experience in wiring these circuits.
This is a skill which will be useful throughout the semester.
EM-4
Colour Codes for Resistors
If the resistor has 4 coloured bands, then the resistance
value can be decoded as follows:
Four Coloured Bands:
First significant
figure (band A)
Second significant
figure (band B)
Number of zeros to
follow (band C)
Tolerance (band D)
(silver or gold)
bands A,B and C
band D
Black
0
Silver
± 10%
Brown
1
Gold
± 5%
Red
2
Orange
3
Yellow
4
Green
5
Blue
6
Violet
7
Grey
8
White
9
Yellow (4)
Orange (3)
Example:
(370,000 ± 5%) Ω
= (370 ± 18) kΩ
Five Coloured Bands:
Violet (7)
Gold (±5%)
If the resistor has 5 coloured bands, then use:
First Sig. Fig.
Second Sig. Fig.
bands A, B, C and D
band E
Use colour code above
Red
± 2%
Brown
± 1%
Third Sig. Fig.
Number of zeros
Tolerance
(brown or red:
thickest band)
Orange (3)
Red (2)
Orange (3)
Red (±2%)
Red (2)
Example
(33,200 ± 2%) Ω
= (33.2 ± 0.7) kΩ
EM-5
Experiment 1
Electric Circuits - A Review?
Safety
Make sure that you have read the safety notes in the introductory section of this manual before
beginning any practical work.
Do not, under any circumstances, attempt to repair any of the equipment should you think it to
be faulty. Rather, turn off the apparatus at the power-point and consult your demonstrator.
If any of the batteries used in this experiment are damaged or leaking do not touch them: they
contain strongly corrosive liquids and will burn your skin. Call your demonstrator and s/he will
clean up the residue.
References
121/2:
Sections 28.5 and 29.3.
141/2:
Sections 28.3 to 28.6; in particular look at equations 28.2, 28.7 and 28.21
Introduction
You probably know people who think the terms “electricity”, “voltage”, “electric power” and
“electric current” are interchangeable and you may find it difficult to clearly explain the difference
between them. This lab exercise explores these basic ideas, emphasising current as a “rate of
flow of charge” and voltage as the energy source sustaining the flow. The exercise should provide
you with the opportunity to review your own understanding of these concepts and to consolidate
your skills in wiring up electric circuits.
During this exercise you will use a common but very useful
device for probing the operation of simple electric circuits - a
light globe. A light globe filament glows due to the
transformation from electric potential energy to light that
occurs as charge passes through it. Its brightness can be
thought of as an indication of the rate of energy
transformation, that is the power being dissipated in the
globe.
I
+ V
– battery
light globe
Figure 1
Recall that:
power
=
charge per second passing though globe
x
energy dissipation per unit charge
=
current
x
voltage
=
I
x
V
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Section A: Batteries and Bulbs
A series of simple circuits comprising batteries and light globes is presented on the following
pages. For each circuit follow this procedure:
(i)
Draw the circuit diagram in your notebook.
(ii)
For each circuit predict the relative brightnesses of each globe in the circuit and predict
how they will compare with the brightness of the globe in circuit A. Make other predictions
about the behaviour of the circuit as requested
(iii)
Verify (or otherwise) your predictions by wiring up the circuit and testing them.
(iv)
Answer the concluding questions.
Circuit A:
We will use this circuit to define some basic quantities:
I0
From here on, we will use:
I0
to represent the current in this circuit.
+ V0
V0
to represent the voltage across the globe in
this circuit.
– battery
L0
to represent the brightness of the globe in
this circuit.
V0
light globe
brightness,
L
Figure 2
Connect up the circuit and observe the brightness L 0.
Important:
In the predictions which follow:
describe brightness in terms of
" = L0 "
or " < L 0 "
or " > L 0 "
only.
describe currents in terms of
" = I0 "
or " < I 0 "
or " > I 0 "
only.
describe voltages in terms of
" = V0 "
or " < V0 "
or " > V0 "
only.
You are not expected to make quantitative statements – in fact it would be difficult to
do so without making measurements of the characteristics of the light globes. Instead
use your understanding of the concepts of voltage and current to help you decide how
each brightness, current and voltage compares to those of the first circuit.
A few hints:
(i)
You should move quickly through these circuits verifying your predictions, but don't
neglect any outcomes which you don't understand. Discuss these with your
partner(s) or demonstrator.
(ii)
It is suggested that you record your results briefly in tabular form, accompanied by a circuit
diagram. For example:
EM-7
Y
•
Investigation
Prediction
Observation
Relative brightnesses:
(A = B) < L 0
(A = B) < L 0
Remove A
B only alight
neither lights!
A
+
V
B
•
Z
Figure 3
(iii)
Note that not all light globes are identical. You will have to decide for yourself whether two
globes of similar brightness should be considered equal or not for the purpose of the
exercise.
Circuit B: Globes in Series
Hint:
Y
•
With the switch closed:
A
V
Remember to compare with Circuit A.
Predict:
What are the relative brightnesses of A and B?
How do they compare with L0?
+
B
-
What is the effect on B of detaching the lead
from one side of A?
•
Z
Questions: Compare the currents at Y, A, B and Z.
How does each compare with I0?
Figure 4
Remember:
How does the voltage across A compare with V0?
In answering the questions and making the predictions compare each circuit
with circuit A.
Circuit C:Globes in Parallel
Hint:
Y
•
With the switch closed:
A
V
Compare with Circuit A.
B
Predict:
What are the relative brightnesses of A and B?
+
How do they compare with L0?
-
What is the effect on B of detaching the lead
from one side of A?
•
Z
Figure 5
Questions: Compare the currents at Y, A, B and Z.
How does each compare with I0?
How does the voltage across A compare with V0?
EM-8
Circuit D: Pairs of Globes in Parallel
Hint:
Y
•
V
With the switch closed:
A
C
Predict:
B
D
Questions: Have these brightnesses been observed in other
circuits? If so, to which are they equivalent?
+
-
Compare with Circuits A, B and C.
What are the relative brightnesses of A, B, C
and D? How do they compare with L0?
Compare the currents at Y, A, B, C, D and Z.
•
Z
How does each compare with I0?
Figure 6
How does the voltage across A compare with V0?
Circuit E: Globes in Series and in Parallel
Hint:
Y
•
V
Compare with Circuits A, B and C.
With the switch closed:
B
Predict:
C
Questions: Have these brightnesses been observed in other
circuits? If so, to which are they equivalent?
A
+
-
What are the relative brightnesses of A, B and
C? How do they compare with L 0?
Compare the currents at Y, A, B, C and Z.
•
Z
How does each compare with I0?
How do the voltages across A, B and C compare
with V0?
Figure 7
Circuit F: Globes in Parallel and in Series
Hint:
With the switch closed:
Y
•
Predict:
A
V
B
•
Z
What are the relative brightnesses of A, B and
C? How do they compare with L 0?
What is the effect of detaching the lead from one
side of A?
+
-
Compare with Circuits A, B and C.
C
What is the effect of detaching the lead from one
side of B?
Questions: Have these brightnesses been observed in other
circuits? If so, to which are they equivalent?
Compare the currents at Y, A, B, C and Z.
Figure 8
How does each compare with I0?
How do the voltages across A, B and C compare
with V0?
Note:
This circuit gives large differences in globe intensities! This can be explained by
recalling (?) that the power dissipated in (and so the brightness of) the globe is equal
to VI.
EM-9
Circuit G:Extra Batteries 1
Hint:
Y
•
A
V
+
-
V
+
B
-
Compare with Circuits A & B. With only one
switch closed, Circuit G is identical to Circuit B.
With both switches closed:
Predict:
What are the relative brightnesses of A and B?
How do they compare with L0?
Questions: Have these brightnesses been observed in other
circuits? If so, to which are they equivalent?
•
Z
Compare the currents at Y, A, B and Z.
How does each compare with I0?
Figure 9
How does the voltage across A compare with V0?
What is the effect of closing only one switch?
Circuit H: Extra Batteries 2
Hint:
Y
•
V
V
With the switch closed:
A
Predict:
B
Questions: Have these brightnesses been observed in other
circuits? If so, to which brightnesses are they
equivalent?
+
+
-
Compare with Circuits A and B.
•
Z
What are the relative brightnesses of A and B?
How do they compare with L0?
Compare the currents at Y, A, B and Z.
How does each compare with I0?
Figure 10
How does the voltage across A compare with V0?
Summary:
Which globes had the same brightness as the original globe in Circuit A? Which globes had the
same brightness as globe A in Circuit B?
Predict the brightness of each globe in the following circuit, again comparing the brightnesses to
L 0. Do not attempt to wire up this circuit.
B
V
+
-
D
G
A
C
E
F
Figure 11
The Further Work section of this exercise will allow you to follow up these light globe circuits by
analysing similar circuits which include fixed value resistors instead of light globes.
EM-10
Section B: Voltage Dividers and Potentiometers
The term “potential divider” usually refers to a circuit which
divides the voltage (potential difference) into two or more
smaller voltages. In the circuits you have already seen today
4.4 V
A
the circuits which included more than one globe in series
divided the total voltage available from the battery between
+
the globes. In terms of energy transformation, the potential
6.0 V
B
C
energy provided by the battery to the charge (6 joule per
1.6 V
coulomb) was “shared” between the globes the charge
passed through. The total energy transformed into thermal
energy and light as charge travelled along a single path
through the circuit was equal to the potential energy change
of the charge. In Circuit F, for example, when a coulomb of charge passed through globes A and B
a total of 4.4 + 1.6 = 6.0 joule of energy was transformed.
These are extremely useful circuits, especially when using transducers such as photocells and
thermistors. Variable potential dividers can be used as volume controls in radios, to control the
brightness of TV screens etc. Later in this section you will design a variable potential divider
circuit.
Consider the circuit below.
A
B
C
Key
+
+ 6 Volts
Battery
D
-
V
E
Resistance
Chain
Voltmeter
F
G
Circuit Diagram
Circuit Picture
Figure 12
Draw the circuit diagram (never the circuit picture!) in your book.
According to the diagram, a potential difference (P.D.) of 6 volts is being applied between the
ends of the resistance chain ABCDEFG. V represents a voltmeter and is used to measure the
P.D. between points to which its terminals are connected. Each resistor in the chain has
resistance R ohms. Find the chain of six resistors on your bench and, using the colour code
information in the introductory notes to this segment, read off R and the tolerance.
EM-11
Exercise:
Predict the following voltages, and write down the resistance between the
points described.
Terminals
Potential Difference
(volts)
Resistance
(ohms)
AA
AB
AD
BF
AG
6.0
Question (a)
Explain the reasoning behind your predictions. If you are completing this
exercise as part of segments 2 to 5 of the year, ie. not the first segment, then
assign an uncertainty to your prediction for VBF.
Question (b)
What result would you predict for a measurement of the circuit current I? If
it’s not segment 1, what is the uncertainty, ∆I?
The voltmeter on your bench has several ranges, eg. 0-10 V, 0-50 V, etc. When
taking a measurement of P.D. across a circuit component, connect the meter in
parallel with the appropriate positive (red) terminal connected to the higher
potential point, and the negative (black) terminal connected to the lower
potential point. This is illustrated in Figure 13.
V
The ammeter (in this case a milliammeter)
should be connected in series with the circuit path
whose current is to be measured as shown in
Figure 14, with the current flowing into the
appropriate positive terminal and out of the
negative terminal.
+
mA
I
Figure 14
Figure 13
Experimental (i)
•
Wire up the circuit and adjust the power supply voltage to obtain 6.0 volts for VAG.
Experimentally determine VBF and I, and quantitatively compare your results with your
predictions from questions (a) and (b).
Question (c)
Do they agree, within confidence limits? If not, what could cause the
discrepancy?
Question (d)
Name a pair of terminals which could be used to supply a nominal P.D. of
(i) 1 volt,
(ii) 2 volts,
and
(iii) 5 volts.
The circuit in Fig. 12 would not supply a continuously variable voltage. However if, instead of
the intermediate terminals BCDEF of the resistance chain, we had a single intermediate
terminal Q which could be moved between A and G, a continuously-variable voltage divider
would be obtained. Such devices are known as rheostats or potentiometers, and are commonly
referred to as "pots". The circuit symbol for a pot is shown in Figure 15.
EM-12
Here the arrow represents the moveable terminal. As you can see, pots
are 3-terminal devices. The resistance between the two end terminals is
fixed and the resistance between an end terminal and the moveable
terminal is proportional to their separation (if the resistor is uniform).
R
P
Ask your demonstrator to show you the pot on your bench.
Experimental (ii)
•
Q
Figure 15
Question (e)
•
Draw a circuit for supplying a continuously variable voltage from
0-3 V, using the power supply and a 500 Ω pot. (Do not include a
voltmeter in your diagram.) Indicate on your diagram the points P
and Q between which the variable voltage appears.
Do you expect the current to vary as the resistance between P and Q changes?
Discuss your circuit design with your demonstrator before wiring it up. Wire up the circuit,
and then test it with your voltmeter.
Question (f)
Does it behave as expected? Describe its behaviour.
Now include an ammeter in series with the 500 Ω pot.
Question (g)
Does the current change as you vary the resistance between P and Q? Is this
what you expected?
Further Work
Each of the circuits in Section A can be simulated by circuits in which a 120 Ω resistor is
substituted for each light globe. The simulation is by no means perfect since the resistance of
the light globe filaments vary with temperature. Under the conditions of this experiment the
resistance of the filaments vary between approximately 75 Ω at their dimmest and 150 Ω at
their brightest.
Exercise:
For each circuit in Section A draw a circuit diagram containing 120 Ω resistors and for each
resistor calculate
(i)
current in the resistor
(ii)
voltage across the resistor
(iii)
power dissipated in the resistor
when 6.0 V batteries are used to supply the circuit.
Rank the resistors from highest to lowest power dissipation, and compare to the relative globe
brightnesses observed during this exercise. Comment on this comparison.
Question (h)
Why would a hot filament have a higher resistance than a room temperature
filament?
EM-13
Experiment 2
Correct Use of Voltmeters and Ammeters
Safety
Make sure that you have read the safety notes in the introductory section of this manual before
beginning any practical work.
Do not, under any circumstances, attempt to repair any of the equipment should you think it to
be faulty. Rather, turn off the apparatus at the power-point and consult your demonstrator.
References
121/2:
Section 29.6 (Ammeter and Voltmeter).
141/2:
Section 28.7.
Introduction
There is more to knowing how to use ammeters and voltmeters than just where to place them in
the circuit. You also need to be aware of the effect your measuring device has on the quantity you
aim to measure. Whenever you use an ammeter or voltmeter to make a measurement in a circuit
the meter itself becomes part of the circuit, affecting the passage of charge through the circuit.
So, current passes through a voltmeter, changing the current in the device you are interested in,
and the potential difference across it. The significance of the effect depends on the circuit, in
particular the resistance of the meter relative to other circuit resistances. Usually the resistance
of the meter also depends on the scale being used. In this experiment you will investigate cases
in which a measuring instrument is being used in an inappropriate situation.
EM-14
Section A: Voltmeters
Experimental (i)
A
22.0 k Ω
B
14 V
+
22.0 k Ω
-
C
22.0 k Ω
D
Figure 1
•
Draw the circuit as in Fig. 1, wire it up and measure VAD.
•
Using this value of VAD, calculate predicted values of V BD, VBC, VCD, and VAB. Include
uncertainties.
•
Now measure V BD, VBC, VCD, and VAB using the 0-50 V range on the voltmeter for all four
measurements AND, where possible, the 0-10 V range.
Question (a)
Can you explain any difference between the predicted and measured values of
P.D.'s? Attempt this first to your demonstrator and then in your book . (If you
cannot do this to your demonstrator's satisfaction, you will have another
chance after answering question (c).)
Construction of Voltmeters
A voltmeter consists of a galvanometer in series with a high resistance R (see Fig. 2 below). The
galvanometer is a sensitive current measuring device which has a deflection proportional to the
current flowing through it.
Galvanometer
Rm
Rg
R g = galvanometer restistance
R m » Rg
Figure 2
Let the current which produces a full s cale deflection in a galvanometer be Ifsd. Then if the meter
is to act as a voltmeter reading from 0 to Vfsd volts, R m must be chosen such that a current Ifsd
flows through the meter when the P.D. between the terminals A and B is Vfsd.
EM-15
Voltmeter
+
10V
50V
Rg
Common
R1
R2
R3
250V
-
Figure 3: Construction of a Voltmeter.
A multi-range voltmeter has a different series resistance for each range, as shown in Fig. 3.
For the voltmeter you are using, full scale deflection occurs for a current of 1 mA passing through
the galvanometer.
Exercise:
(i)
Calculate the total resistance of the voltmeter for each of its ranges and make a
table of resistance versus voltage range.
(ii)
Voltmeters are generally rated as so many ohms per volt. Your voltmeter is rated as
1000 ohms per volt. Explain what this means to your demonstrator and in your
book .
(iii)
If you were unable to answer question (a) to your demonstrator's satisfaction earlier,
can you do so now? If not, don't give up! Try again after completing the next
exercise.
Resistances in Parallel
Consider a set of n resistances connected in parallel:
I
I1
R1
I2
R2
I
B
A
In
Rn
Figure 4
The P.D. across each resistance is the same, (ie. VAB)
EM-16
Hence it follows from Ohm's law that:
I1 = VAB/R1,
I2 = VAB/R2 ,
In = VAB/Rn
ie. the currents are inversely proportional to the resistances.
Also,
I = VAB/R
where R is the equivalent resistance of R 1, R2,....., Rn in parallel.
However,
I = I1 + I 2 + ......+ In ,
and so, therefore:
1/R = 1/R1 + 1/R 2 + .....+ 1/Rn .
Note that a set of resistances in parallel acts as a current divider, whereas a set of resistances in
series acts as a voltage divider.
The situation shown below in Fig. 5 is equivalent to measuring VBD with the voltmeter on the
0-10 V range.
A
22.0 kΩ
+
-
B
VAD
44.0 kΩ
10.0 kΩ
D
Figure 5
Exercise
Calculate RBD, VAB, and VBD, taking for VAD the voltage you measured for VAD
earlier. Now answer question (a) quantitatively. If you cannot, then seek help
from your demonstrator before going on.
Question (b)
Why would the disagreement referred to in question (a) not occur in
measurements using the chain of six resistors used in Section B of
Experiment 1?
EM-17
Section B: Ammeters
+
12 V
47 Ω
-
22 Ω
3.3 kΩ
Figure 6
Experimental (ii)
•
Use your milliammeter to measure the current flowing through each of the resistances in
the circuit shown above. What range of your milliammeter will you use? Indicate on your
circuit diagram where you will connect your milliammeter for each measurement.
Question (c)
Does the current measured in the 3.3 kΩ resistor equal the sum of those
measured in the 47 Ω and 22 Ω resistors? If not, account to your
demonstrator for any difference. If you cannot, try again after answering
question (e).
Construction of Ammeters
Galvanometers are current measuring devices which generally give full scale deflection for very
small currents. When it is required to measure larger currents than this, it is necessary to divert
some (often most) of the current along an alternative path, RS, called a shunt.
Ammeter
Rs
A
Rg
B
Figure 7: Construction of an Ammeter
If the meter is to be used to measure currents from 0 to Io amps, and the galvanometer gives full
scale deflection for a current Ifsd, the resistance of the shunt must be chosen such that a fraction
Ifsd/Io of the total current passes through the galvanometer.
The galvanometer in your milliammeter gives full scale deflection for a current of 1 mA; its
resistance, R g, is marked on the back of the meter.
EM-18
Exercise:
Calculate the resistance of the shunt when the meter is used as a 0-5 mA
meter. Hence calculate the resistance between the terminals of the
milliammeter on this range.
Question (d)
Were any of the meter readings obtained experimentally a reliable measure of
the current flowing before the meter was inserted?
Question (e)
Show that this meter resistance value accounts quantitatively for the meter
reading you obtained in the experiment for the current in the 22 Ω resistor.
Hint: you should try and obtain an expression for the current in each branch
as a fraction of the total current. Remember if you are having any trouble your
demonstrator will help you.
Question (f)
What are your conclusions regarding the correct usage of voltmeters and
ammeters? (This question may be answered as part of your overall conclusion
to the experiment.)
Further Work
To give a 0-25 mA range as well without using changeable shunts, your meter is wired like this:
5mA
Common
Rg
R1
R2
25mA
Figure 8
Exercise:
(i)
Calculate the magnitude of R 1 and R 2 for your meter.
(ii)
Hence calculate the resistance between the terminals of your milliammeter for the 025 mA range.
Question (g)
In Section B of Experiment. 1, what effect will the inclusion of the ammeter
resistance have upon the current in the circuit? Does your calculated value for
the current now agree with the experimental data?
EM-19
Experiment 3
Investigating Resistance - Wheatstone's Bridge
Safety
Make sure that you have read the safety notes in the introductory section of this manual before
beginning any practical work.
Do not, under any circumstances, attempt to repair any of the equipment should you think it to
be faulty. Rather, turn off the apparatus at the power-point and consult your demonstrator.
References
121/2:
Sections 29.8 (Wheatstone Bridge) and 28.4.
141/2:
Section 27.4 (Calculating the Resistance).
Introduction
The measurement of resistance using an ohmmeter is a very commonly used technique.
However, the inherent accuracy of this method is limited by the reliability of reading the scale of
the milliammeter (see Experiment. 2).
Many of the moving coil meters are reliable to only 5% and few are reliable to better than 2%.
Even with a high precision calibrated meter, the accuracy attainable will be limited by the
accuracy to which the scale can be read; for example, on its 0-5 mA range, your milliammeter can
be read to > 0.01 mA, which for a reading of 1 mA is > 1%.
In this experiment you will investigate a method of measurement (known as the null detection
method) using a circuit known as Wheatstone’s Bridge, which avoids the dependence on a meter
reading. You will then use this circuit to accurately measure very low resistances and hence
investigate the nature of resistance. Consider the circuit shown below (figure 1).
A
Remembering the idea of potential dividers from
experiment 1, we can say that
R1
R3
B
C
R2
R4
D
Figure 1
VAB
R
= 1
VBD R2
On the other side of the parallel circuit we can show that
VAC R3
=
VCD R4
EM-20
Question (a)
Suppose B and C are joined via a key and a galvanometer, as shown in Fig. 2.
What conditions are necessary for there to be zero current in the galvanometer
when the switch is closed? (How does VAB compare to V AC? How do VCD and V BD
compare?)
Question (b)
What is then the relationship between the ratios
R1
R3
and
?
R2
R4
I
A
R1
R3
B
C
R2
R4
D
I
Figure 2
Under these conditions, the bridge is said to be balanced.
If R1, R2, and R4 are accurately known, high-precision resistors, then an unknown resistance (R3)
may be accurately found using the equation you derived in question (a). (For convenience, the
ratio R1/R2 is normally made an integer power of ten, using the ratio box.)
EM-21
Section A: Balancing the Bridge
The aim is to measure R3 by finding the value of R4 for which the bridge is balanced, ie for which
no detectable current passes through the galvanometer.
This is known as the null detection method of measurement. We can adjust R4 until we detect
no current between B and C (using the galvanometer).
We will use the circuit shown below (figure 3).
I
A
R1
Ε
R3
B
C
R2
R4
D
I
Figure 3
It is important to include the key (touch switch) so you do not leave the current flowing through
the galvanometer. The galvanometer is not designed to have a significant current flowing
through it for any length of time.
The principle underlying the use of this circuit is very similar to the beam balance used for
measuring an unknown mass. You add known masses to one side of the balance, and when the
beam is horizontal the unknown mass is equal to the known mass.
The method you will use, in the following experimental sections, for balancing the bridge (and
thus determining an unknown resistance) can be summarised as
1.
Place the unknown resistance in the position R3 in the above circuit.
2.
Set the ratio box to the best value for the ratio R1/R2. Notice that the decade box allows
you to set its resistance to values from 0Ω to 11110Ω . Ideally you would like the value of
R4 when balanced to lie between 1000Ω and 11110Ω these values (this gives you a
maximum number of significant figures in your measurement of the unknown resistance
because every dial on the decade box is then used).
3.
Set R4 to a value close to its expected value.
4.
Adjust the least sensitive dial of the decade box (ie. 1000 Ω), touching the key switch at
each value to find the two values of R4 about which the direction of the current changes
5.
Choose the lower of these two values, then adjust next most sensitive dial (100 Ω) as
above. Continue this until you find the best value of R4.
EM-22
The smallest increment on the decade box (R4) is 1Ω , so it is possible for the balanced condition
to occur between two values of R 4. In this case the galvanometer will indicate current flow one
way for one value of R4, then current flow the other way for the next value (say R4+1Ω ). Thus we
know the value required for balance is between R4 and R 4+1Ω . The relative sizes of the
deflections may be used for gaining a further decimal place in our estimate of the balanced value
for R4. In practice for this experiment getting R4 within 1 Ω will suffice.
Experimental (i)
•
Using one of the nominally 2.2kΩ resistors on your bench (as R 3), balance the bridge, using
the method described on the previous page. Record the values of R1, R2, and R4. Use these
to give an accurate estimate of the nominally 2.2kΩ resistor’s actual resistance.
Remember to include uncertainties.
Question (c)
Will your choice of voltage to use affect your measurement? Discuss with your
demonstrator the possible effects of a very large voltage or very small voltage
on your results. Then choose a voltage to use.
Section B: Resistance - What is it?
In this section you will determine the relationship between resistance and length, and between
resistance and diameter of a wire. You are provided with six resistance wires made of the one
material (Nichrome V), but of varying diameters, plus a single wire with which you can measure
resistance as a function of length, and a micrometer for measuring the diameters of all seven
wires.
•
Before taking any measurements with the Wheatstone's Bridge, determine the
approximate resistance of each wire using the multimeter provided.
Question (d)
What ratio R 1/R2 will you use? Therefore, what will be the approximate values
of R4 (the decade box) for each wire?
Resistance as a function of length
Experimental (ii)
•
Using various lengths of the single wire as R 3 (going up in, say, 10 cm intervals), balance
the bridge and tabulate your results as before; then plot a graph of R3 against L. Make
sure you measure the diameter of the wire.
The resistivity of a material, ρ, is defined by
R=
ρL
,
A
where A is the cross-sectional area of the wire.
Determine ρ and its uncertainty and compare your estimate with the known value of
ρ = 1.08 x 10-6 Ω m, at 20°C.
EM-23
Resistance as a function of diameter
Experimental (iii)
•
Using one of the six different diameter wires at a time (as R3), balance the bridge and
tabulate your results. Remember to include uncertainties. You should re-measure some of
your results to determine how reproducible the measurements are (and hence their
uncertainty).
Assuming R ∝ d n , then R = kdn . Thus,
log R = log k + log dn
= log k + n log d.
Using your tabulated results, plot a graph of log R3 versus log d.
Determine n and its uncertainty from your graph, and thus conclude what your experimentallydetermined relationship between resistance and the diameter of a wire is.
Further Work
Ohmmeters
The current flowing in a circuit depends on the resistance in the circuit. This fact may be
exploited to construct a meter for measuring resistance (this is how the multimeter you used for
your initial estimates worked).
Such a device is called an ohmmeter. Clearly, it must include:
1.
a battery (or power supply) to maintain the current; and
2.
a meter to read the current.
Consider the circuit below:
1.5 V
+
A
-
B
mA
+
Figure 4
The idea is to arrange things such that the scale of the milliammeter corresponds to a range of
resistance from 0 to ∞ inserted between A and B.
Question (e)
When AB is open circuited, ie. the circuit is broken there, what is the reading
of the milliammeter? What is the resistance between A and B?
EM-24
Question (f)
When AB is short circuited, what determines the reading of the milliammeter?
What is the resistance between A and B?
Question (g)
To satisfy the criterion stated above, that the milliammeter scale should
correspond to a resistance range from 0 to ∞, what would you like the
milliammeter to read when AB is shorted? How can you make it do so?
Experimental (iii)
•
The aim of this section is to convert the milliammeter into an ohmmeter, and to calibrate
its scale. Before wiring up the circuit it will be necessary to check that the power rating of
the pot (the value of which is given in most cases on the side of the pot) will not be
exceeded. When you have done so, wire up the circuit, and set it up with R suitably
adjusted for the 0-5 mA range.
•
By placing a decade box between the points A and B, you can measure the current for a
range of resistances. You should adjust the decade box to give you a nice spread of
currents (between 0 and 5 mA).
•
Hence draw a calibration graph of r versus I, for r from 0-2000 Ω , so that the circuit may
be used as an ohmmeter for the 0-5 mA range.
•
On your graph construct a resistance scale for your meter by placing your experimentallydetermined resistance values either on or alongside your current axis in their appropriate
positions. Then compare this with the scales of the multimeter on your bench.
•
Comment on why this method is less accurate than the Wheatstone’s Bridge for measuring
resistance.
Your milliammeter has two ranges. If, in setting up the ohmmeter, you were to use the 0-25 mA
range, what effect would it have on the useful range of your ohmmeter? Check your prediction
experimentally