Experiment 2g
Class:
Name:
(
) Date:
2g Using a voltmeter to measure voltage
across resistors
Objective
To study the effect of internal resistance of a voltmeter in measuring
voltage.
Background information
1
The reciprocal of equivalent resistance of resistors connected in
parallel is equal to the sum of the reciprocal of individual resistances
of them. The equivalent resistance is always lower than each
individual resistance.
2
Voltmeters are not ideal in reality. They have an internal resistance
which affects the voltage they measure.
Apparatus
❏ 2 resistors (both 100 kΩ)
❏ 1 switch
❏ 1 voltmeter
❏ several connecting leads
❏ 1 battery box (3 V)
Procedure
✐ The e.m.f. of
the battery and the
resistances of the
resistors can be changed
to other values available.
1
Set up the apparatus as shown in Figure 2g-1:
(a) Connect two 100-kΩ resistors (R1 and R2) in series with a
3-V battery box and a switch.
(b) Connect a voltmeter across one of the two resistors.
battery box
switch
voltmeter
R1 = 100 k8
R2 = 100 k8
V
Fig 2g-1
40
New Physics at Work (Second Edition)
100-k8 resistor
100-k8 resistor
© Oxford University Press 2007
Class:
Name:
(
Experiment 2g
) Date:
2
Measure the voltage V ′ across resistor R1 using the voltmeter.
✎
1.2
Voltage V ′ across resistor R1 = ___________
V
3
Calculate the theoretical value of voltage V across resistor R1.
✎
3
Theoretical voltage across resistors R1 and R2 = ___________
V
100 000 + 100 000
Equivalent resistance of resistors R1 and R2 = ___________________
200 000
= ___________________
Ω
Theoretical current I of the circuit =
3
200 000
___________
0.000 015 A
= ___________
100 000
Resistance R of resistor R1 = ___________
Ω
Theoretical voltage V across resistor R1 = IR
0.000 015 × 100 000
= _____________________
1.5
= _____________________
V
Discussion
✎
What is the resistance of an ideal voltmeter?
Infinity
✎
✐ When the voltmeter
is connected, the current
flowing in the circuit is
not the same as that
before. To see why the
voltage across resistor
R1 decreases, Ss should
compare the equivalent
resistance across R1 and
the resistance of R2, and
notice that they ‘share’
the same total amount
of voltage provided by
the battery. The larger
the resistance, the larger
the portion of voltage the
resistor ‘shares’.
Compare the theoretical value V and the experiment value V ′ of
voltage across resistor R1. Account for the difference.
The theoretical value V is much larger than the experiment value V′.
A voltmeter has a large internal resistance which is not infinite. When it is connected
in parallel with the resistor R1, the equivalent resistance across the resistor decreases.
Therefore, the voltage across the resistor, which is the measured voltage, decreases.
large
A practical voltmeter has a _______________________
internal
resistance instead of infinity. When it is connected in parallel
with a resistor in a circuit, the equivalent resistance across the
decreases
resistor ________________________
and the measured voltage is
smaller
________________________
than the theoretical voltage across the
resistor.
New Physics at Work (Second Edition)
© Oxford University Press 2007
41
Experiment 2g
Class:
Name:
(
) Date:
Further thinking
✎
How does the accuracy of a voltmeter in measuring voltage change
with its internal resistance? Explain your answer.
The smaller the internal resistance of a voltmeter, the lower its accuracy.
When the internal resistance of a voltmeter decreases, the equivalent resistance
across the resistor decreases. Therefore, the voltage across the resistor, which is
the measured voltage, decreases. In this case, the difference between the measured
value and the theoretical value of voltage increases.
✎
How will the experimental value V ′ of voltage across resistor R1
change if this experiment is repeated with two 100-Ω resistors?
Explain your answer.
The experimental value V′ will become larger and closer to the theoretical value.
In this case, the resistance of the voltmeter is much larger than that of the resistor
and the effect on the measurement will become smaller.
42
New Physics at Work (Second Edition)
© Oxford University Press 2007