Moving Coil Meters
Although most modern voltmeters and ammeters are
digital, analogue meters are still widely used in the electrical
engineering industry. Although analogue meters are sometimes
considered old hat, you can still buy one for as little as £3.50
(€4.50). An analogue meter has a scale with a
pointer. People like analogue instruments. Most cars
still have them. Although the most modern aeroplanes have
touchscreen computer technology for the pilots, these still show images
of analogue meters, rather than columns of numbers. Why?
Because pilots get a better picture of the reading of the instrument and
compare it with what it should be. Humans, like all other animals,
are analogue.
A digital instrument can read to several decimal places,
while an analogue meter usually reads to no more than 2 decimal places.
For most purposes, that is quite adequate.
Many students think that digital meters with their direct
readout are more accurate than analogue meters. They may be
more precise, but, unless they have been calibrated correctly,
they may not be accurate. Instruments with certified
calibration are very expensive indeed, because it takes time to verify
the calibration.
Many students have a lot of difficulty with analogue
instruments, especially if scales need to be converted. For
example, a meter may have a scale that reads from 0 to 100. If it
is used to measure 5.0 V, the 100 mark means 5.0 V, while the 60 mark
represents 3.0 V.
In this section, we will look at how moving coil
(analogue) meters work, and how they can be used to measure voltage,
current, and power.
I have used this meter since I got it as a teenager.
And it still works.
A moving coil meter works by using a very light coil
connected to a needle that acts as a pointer. The coil is placed
over a stationary cylinder of magnetic material between the
circular poles of a magnet. This has the effect of making the
field as close to radial as possible, ensuring a uniform torque.
The torque from the current is balanced by a torque in
the opposite direction from a very fine hair spring. There
is one of these at each end of the coil. It also acts as a
conductor for the current going into the coil. The picture below
shows the idea in a real meter.
We know that the torque on the coil is given by:
t = BANI
There is a torque in the opposite direction from the hair
spring. We know that for a linear spring, Hooke's Law
applies:
Force (N) = Spring constant (N m^{1}) ×
extension (m)
For a spring that's a flat coil spring, a similar
rotational formula applies:
Torque (N m) = torsion constant (N m rad^{1}) ×
angle turned (rad)
In physics code, the formula is written:
t = kq
Remember that the angle is in radians.
It does not take a genius to equate the two
relationships:
kq = BANI
Worked Example
A meter has a coil consisting of 500 turns of
very thin copper wire on a very light rectangular former 1.0
cm × 2.0 cm. It is held in place on a shaft where the
friction is negligible. Its motion is opposed by two
very fine hair springs of which the torsion constant is 1.5
mN m rad^{1} for each
spring. The magnetic field has a flux density of 0.35
T.
Calculate the angle through which the needle
turns when a current of 50 mA
flows. 
Answer
Formula rearranged:
q = (0.35 T
× 2.0 × 10^{4} m^{2} ×500 × 50 × 10^{6}
A) ÷ (2 × 1.5 × 10^{6} N m rad^{1})
There are two springs...
q = 0.58
rad (= 33.4 ^{o})

Remember that if the angle is given in degrees, you need
to convert to radians.
1 rad = (360 ÷ 2p)^{o}
» 57.3^{o}
1^{o} = (2p
÷ 360) rad
Question 4 
A moving coil meter has a
coil of dimensions 1.5 cm × 2.0 cm. The coil has 600 turns
and is placed in a magnetic field that has a flux density of
0.25 T. The coil is mounted by two springs of torsion
constant 1.2 mN m rad^{1}
and is deflected by 40^{o} when a current passes through
it.
Calculate the current flowing in
the coil. 

The currents that are used in
moving coil meters are very small. A common value for the full
scale deflection of a moving coil meter in a college physics laboratory
is 100 microamps. 