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Circuit Electricity 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.
Prelab Questions
These questions are designed to start you thinking. Answer them as best you can after reading
the exercise, and remember them as they should help you complete the rest of the prac.
1. Should a voltmeter have a large or small internal resistance for it to have a small effect on the
passage of charge through a circuit? Explain your reasoning. (Hint, where in the circuit do
we place a voltmeter?)
2. Should an ammeter have a large or small resistance? Why?
3. We can think about the effects of including a measuring device in a circuit by considering the
change in the circuit’s “effective resistance”. A voltmeter gives a reading of the voltage
between its terminals. If the inclusion of a voltmeter in a particular circuit lowered the
effective resistance between the voltmeter terminals, how would this affect its reading?
Physics 121/2 and 141/2 Laboratory Manual
C-15
Section A:
Voltmeters
Uncertainties
Whenever we take an experimental measurement we must also consider any errors associated
with it. In this experiment you will need to take into account:

Reading errors – How do I estimate the uncertainty in a measurement? Refer to page 16 of
you manual for advice on this.

Calculating confidence limits – How do I calculate the uncertainty in a determined
quantity? Refer to page 20 of your manual.
Experiment (i)
A
22.0 k
B
12 V
+
22.0 k
-
C
22.0 k
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 VBD, VBC, VCD, and VAB. Include
uncertainties.

Now measure VBD, 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)
C-16
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).)
Physics 121/2 and 141/2 Laboratory Manual
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 that has a deflection that is proportional to
the current in it.
Galvanometer
A
B
Rm
Rg
Rg = galvanometer resistance
Rm » Rg
Figure 2
Let the current which produces a full-scale deflection in a galvanometer be Ifsd. Then if the meter
is to act as a voltmeter reading from 0 to Vfsd volts, Rm must be chosen such that there is a current
of Ifsd in the meter when the P.D. between the terminals A and B is Vfsd.
+
Voltmeter
10V
Common
50V
Rg
R1
R2
R3
250V
-
Figure 3: Cons truction of a Voltmeter.
A multi-range voltmeter has a different series resistance for each range, as shown in figure 3.
For the voltmeter you are using, full-scale deflection occurs for a current of 1 mA in 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.
Physics 121/2 and 141/2 Laboratory Manual
C-17
Resistances in Parallel – an aside
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)
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 R1, R2,....., Rn in parallel.
However,
I = I1 + I2 + ......+ In,
therefore:
1/R = 1/R1 + 1/R2 + .....+ 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 V BD with the voltmeter on the
0-10 V range. The voltmeter is represented by the 10.0 k resistance.
A
22.0 k
+
-
B
VAD
44.0 k
10.0 k
D
Figure 5
C-18
Physics 121/2 and 141/2 Laboratory Manual
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?
Section B:
Ammeters
+
12 V
47 
-
22 
3.3 k
Figure 6
Experiment (ii)

Use your milliammeter to measure the current in 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 k resistor equal the sum of those
measured in the 47  and 22  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 that 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, R S, 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.
Physics 121/2 and 141/2 Laboratory Manual
C-19
The galvanometer in your milliammeter gives full scale deflection for a current of 1 mA; its
resistance, Rg, is marked on the back of the meter.
Consider using the meter as a 0-5 mA meter. What is the maximum current in
the shunt? What must be the value of the shunt resistance? Hence calculate the
resistance between the terminals of the milliammeter on this range.
Exercise:
Question (d) Show that this meter resistance value accounts quantitatively for the meter reading
you obtained in the experiment for the current in the 22  resistor. Hint:
Draw the circuit, including the ammeter and its resistance. Try to obtain an
expression for the current in each branch as a fraction of the total current in
the circuit. Remember, if you are having any trouble your demonstrator will
help you.
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.)
Question (e)
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 R1 and R2 for your meter.
(ii)
Hence calculate the resistance between the terminals of your milliammeter for the 025 mA range.
Question (f)
C-20
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?
Physics 121/2 and 141/2 Laboratory Manual