A‐V‐Ω Meter (Multimeter)
Physics Laboratory
1.
1 Scale
2. Pointer
3. Zero position
adjuster
4. Zero-ohm
position adjuster
5 Range selector
5.
6. Full-scale
deflection value
7. Input terminals
HOC 203
Multimeters and CROs
1
Taking a reading
2
A swing coil meter
y Select a suitable range to produce a maximum deflection.
1. The pointer moves
with its pivot at the
swinging coil
y Range corresponds to the full‐scale deflection (f.s.d.)
of the meter.
2. An iron core which
converges the
magnetic field lines
3. Pole piece of the
permanent magnet
If f.s.d. is 50 V,
then the reading
is 47 V
4. The swinging coil
5. Returning hairspring.
3
4
1
Voltmeter
Characteristics
y Input impedance (internal resistance) in the coil determines the current.
y Current in coil produces a torque in the presence of a magnetic field.
y The iron core converges the magnetic lines in the radial direction.
y Shape of the two pole pieces allows field lines to be always parallel to the plane of the coil. Hence torque produced depends only on the strength of
d d d
d l h h f
the current.
y Deflection of pointer ∝ torque produced ∝ current flowing in coil ∝ applied voltage.
y Large internal resistance (or input impedance for A.C. measurement).
y It usually differs for different ranges. It is about 20
It usually differs for different ranges It is about 20
kΩ V‐1.
y Can measure D.C. as well as A.C. voltages.
y Internal resistance of various types of voltmeter
y Vacuum tube voltmeter (VTVM)
: 11 MΩ
y Cathode ray oscilloscope (CRO)
: 10 MΩ
y Digital voltmeter (DVM) : 10 MΩ
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6
Effects of internal resistance
Example
y The combined resistance of r & R is always smaller y The voltage across the 1MΩ resistor is measured by a voltmeter having an internal resistance of 20 kΩ
g
V‐1. What are the readings when 10 V f.s.d. and 2.5 V f.s.d. are used?
then r or R. Hence the insertion of the voltmeter always lowers the potential between A & B.
rR
Rr
≈
= r if R >> r
r+R R
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8
2
2.5 V f.s.d.
10 V f.s.d.
y Internal resistance =
y
10 x 20 kΩ = 200 kΩ.
y Internal resistance =
1M × 200k
= 0.167 MΩ
1M + 200k
0.167
× 6 V = 0.86 V
∴ voltage across AB =
1 + 0.167
Resistance across AB =
y
2.5 x 20 kΩ = 50 kΩ.
Resistance across AB = 0.047 MΩ
0.047
∴ voltage across AB =
× 6 V = 0.27 V
1 + 0.047
9
Changing Voltage Range
10
To Measure High Tension
Vm
Vm
Rm
Im
Rs
Rm
Im
Rs
V
y A series resistor Rs is connected.
y V ~ Im(Rm+ Rs)
y e.g. if full scale deflection requires 1 mA, and Rm = 1000 Ω, then full scale voltage is ImRm = 1 V.
V
y Rs becomes a high voltage probe with resistance as high as 10 MΩ or 100 MΩ.
or 100 MΩ
y If Rs = 9000 Ω, then full scale deflection occurs at V = 10 V.
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12
3
Rectification
D.C. and A.C. measurement
y D.C. voltage is applied directly to the swinging coil.
A.C. voltage has to be converted to D.C. by the yA
C voltage has to be converted to D C by the following two steps before connected to the coil.
y Rectification
y Filtering
(a) Half-wave rectifier
(b) Full-wave rectifier
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14
Ammeter
Filtering
y A special circuit used to smooth out the oscillating pattern, or ripples so that a stable and constant D.C. voltage is fed to the coil.
y The final reading is the root‐mean‐squared (R.M.S.) value of the A.C.
y Very small internal resistance
y Can measure D.C. and A.C. currents
y The addition of the ammeter will inevitably increase the total resistance between AB and therefore lowers the current flow.
y
i=
15
V
V
≈
r+R R
if
R >> r
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4
D.C. and A.C. current
Changing Current Range
Rm
Im
I
Is
y The ammeter can be thought as a voltmeter Rs
measuring the p.d. between points a & b.
y Hence description on D.C. and A.C. voltage measurement is also suitable for d C and A C
measurement is also suitable for d.C. and A.C.
current measurement
y Scale is linear, i.e. „
„
deflection ∝ magnetic torque ∝ current
17
A.C. clip‐meter
A shunt resistor Rs is connected.
Since IsRs = ImRm
I = Im+Is = Im+ImRm/Rs = Im(1+Rm/Rs)
e.g. if full scale deflection corresponds to 1 mA, then when Rm = 999 Ω and Rs = 1 Ω, full scale deflection corresponds to ?
1A
18
Changing magnetic flux
y The wire carrying the A.C. current is clipped by the meter.
b
h y The changing current will produce a changing magnetic flux in the clip, hence inducing an emf in the clip.
f i th li
19
ρ ρ
dΦ
A ⋅ dB
Induced emf = ε = −
=−
dt
dt
where Φ = magnetic flux enclosed by A
ρ
A = cross - sectional area of the coil
ρ
B = magnetic flux density
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5
Notes on clip‐meter
A.C. Parameters
y The wire needs not be placed at the centre of the clip.
y Peak value: the amplitude or maximum value
y The induced emf is dependent on the rate of change of
the magnetic field lines. For use in Hong Kong, it has to be calibrated for 50 Hz.
g
y Average value: i=
1 T
1 T
i( t )dt and V = ∫ V ( t )dt
∫
0
T
T 0
y Effective value: If a DC current and an AC current are applied to the same resistor R. Within one period, they produce equal thermal heating:
T
I 2 RT = ∫ i 2 ( t )Rdt or I =
0
Similarly,
V=
1 T 2
i ( t )dt
T ∫0
1 T 2
v ( t )dt
T ∫0
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22
Using an ohm‐meter
Ohm‐meter
V∝
1. Ohm-meter
r
r +R
Hence,
2. Voltmeter
where r & R are comparable
deflection ∝ current ∝
r
R+r
3. Range selector
4. Internal battery
5 Unknown
5.
y R & r should be comparable in value, i.e. when R
R & r should be comparable in value i e when R
is large, r is also chosen to be large and vice versa.
y Set zero by shorting the two terminals.
y Scale is usually non‐linear.
resistance R
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24
6
Scale of an ohm‐meter
Precautions
y Choose the suitable mode – A.C. or D.C., voltage or
y The resistance is the meter reading multiplied by the range factor.
y In (a), if x10 kΩ is used, resistance is 7 x 10 k which is 70 kΩ.
y In (b), the same resistance is measured in the x 1 kΩ range.
current or resistance.
y Note that the pointer is at the zero position of the scale
when the two input terminals are shorted together. Adjust
the position if necessary.
y To measure D.C., connect the terminals such that current
enters the meter from the ‘+’ terminal and leaves from the
‘-’ terminal.
y Always start with the range that gives the smallest
deflection of the meter. Then decrease the range
stepwise until suitable deflection is obtained. Remember
that larger deflection gives smaller percentage error.
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26
Sketch of a Cathode Ray Tube
Precautions for ohm‐meters
Electron gun
Fluorescent
screen
y Adjust the zero-ohm position by shorting the two terminals
y
y
y
y
together.
Note that the internal battery has its positive pole
connected to the ‘-’ terminal of the meter such that current
flows out from that terminal to the external resistor. This
point is especially important when the meter is used to
measure diodes or transistors.
Do not measure the resistance of a component that is
connected to a circuit.
Always switch off the power supply to that component.
After measurement, turn the range of the meter to the
other modes such as voltmeter or ammeter to prevent
accidentally draining the internal battery.
27
Luminous
trace
Electron
beam
Deflecting
plates
Sine wave
Sawtooth
wave
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7
Controls of a CRO
Lissajous Figures
y Compare voltages; phases and frequencies
y Intensity
y Focus
y Voltage range selector (V cm‐1 or mV cm‐1)
y Time base (s cm‐1, ms cm‐1 or μs cm‐1)
y X‐shift and Y‐shift
y Y‐input
y X‐input
Xi
t
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30
Other Controls
y Sweep mode: auto, normal, single
y Source Source – Ch1, Ch2, line, external
Ch1 Ch2 line external
y Coupling – AC, DC, TV, HF rej
y Slope ‐ +ve, ‐ve
y Triggering level
y Double beam display
y Alternating mode: good for fast pulses
y Chopping mode: good for low frequency waves
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