Download Lesson 14A

Ammeter and Voltmeter
An ammeter is used to measure the current through a resistor R that forms part of a
circuit. It must be connected in series to the resistor so the current will go through
it. In order not to disturb the rest of the
circuit, the combination of the resistor
and the ammeter must have an equivalent
resistance similar to the original
resistance R . If RA is the resistance of the
ammeter, the condition
Req = R + RA » R
requires that the ammeter has very small resistance.
A voltmeter is used to measure the voltage
across, or the potential difference between the
two leads of, a resistor. Again in order not to
disturb the rest of the circuit, the combination of
the resistor and the voltmeter must have an
equivalent resistance similar to the original
resistance. If RV is the resistance of the
voltmeter, the condition
1
1 1 1
= +
»
Req R RV R
requires that the voltmeter has very large resistance.
At the heart of the ammeter or voltmeter is a
galvanometer. For our purpose, it is just a device
that senses the current when connected into a
circuit. It has resistance RG . The maximum current
that goes through it without damaging it is
denoted by IG,max , and is related to the maximum
voltage VG,max across it by Ohm’s law:
VG,max = IG,max RG
In an ammeter, a resistor called the shunt resistor RS is connected in parallel with a
galvanometer in order to reduce the overall resistance. The ammeter resistance is
therefore given by
1
1
1
=
+
RA RG RS
The requirement of small resistance is satisfied if RS is very small, so that RA » RS .
When an ammeter is used to measure the maximum current I max it can handle, the
galvanometer current reaches the value IG,max . Referring to the diagram below,
where it is seen that the galvanometer and the shunt resistor share the same voltage
difference, we have
( Imax - IG,max ) RS = IG,max RG = VG,max
Because RS << RG , we have I max >> IG,max . It follows that
I max =
VG,max
RS
Thus different scales for the ammeter can be chosen by using different shunt
resistances.
In a voltmeter, the shunt resistor is connected in series with the galvanometer.
Therefore
RV = RG + RS » RS
The last approximation is because a voltmeter should have very large resistance so
that RS >> RG . When it is used to measure the maximum voltage Vmax it can handle,
the same current IG,max goes through the galvanometer and the shunt resistor, while
the voltages across them are VG,max and Vmax -VG,max respectively. From Ohm’s law:
Vmax -VG,max VG,max
=
= IG,max
RS
RG
Since RS >> RG implies Vmax >> VG,max , it follows that
Vmax = IG,max RS
Again different scales for the voltmeter can be chosen by using different shunt
resistances.