DC and AC Meters

1
Chapter 2

• DC and AC Meters

2
Structure for Chapter 2

• Part 1 (DC)

• Part 2 (AC)

• Introduction to DC meters
• D Arsonval meter movement
• DC ammeter
• DC voltmeter
• DC ohmmeter

• Introduction to AC meters
• D Arsonval meter movement (half-wave
  rectification)
• D Arsonval meter movement (full-wave
  rectification)
• Loading effects of AC meter

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Part 1 DC Meters

• Meters

Digital Meters Measure the continuous voltage/
current signal at discrete points in time. The
signal converted from analog signal (continuous
in time) to a digital signal (discrete instants
in time)
Analog Meters Based on the dArsonval meter
movement which implements the readout mechanism.
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IntroductionHow can we measured current and
voltage?
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Ammeter, Voltmeter and Ohmmeter?

• DC Ammeter The shunting resistor Rsh and
  dArsonval movement form a current
  divider
• DC Voltmeter Series resistor Rs and dArsonval
  movement form a voltage
  divider.
• Ohmmeter Measures the current to find the
  resistance

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DC Ammeter

• DArsonval movement, Rm shunt resistor, Rsh
• To limit the amount of the current in the
  movements coil by shunting some of it through Rsh

Rsh resistance of the shunt Rm
internal resistance of the meter
movements (movable coil) Ish
shunt current Im full scale deflection
current of the meter movement I
full-scale deflection current for the ammeter
Parallel symbol
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DC Ammeter (contd)
Vm ImRm Vsh IshRsh Vsh Vm IshRsh ImRm Rsh
ImRm / Ish (O) ----(a) I Ish Im Ish I
Im Therefore, Rsh ImRm/(I Im) Purpose I gtgtn
Im , n multiplying factor nI/Im I nIm
---(b) Substitute b to a Rsh ImRm/(nIm
Im) Rsh Rm/(n-1) -----(c)
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Example 1 (DC ammeter)
Example 1 DC Ammeter

• A 100uA meter movement with an internal
  resistance of 800O is used in a 0 - 100 mA
  ammeter . Find the value of the required shunt
  resistance.
• Solution
• n I/Im 100 mA / 100 µA 1000
• Thus,
• Rsh Rm / (n 1) 800 / 999 0.8 O

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The Aryton Shunt
Most sensitive range

• Used in multiple range ammeter
• Eliminates the possibility of the moving coil to
  be in the circuit without any shunt resistance

Rsh Ra Rb Rc
----(c)
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The Aryton Shunt (contd)
At point B, (RbRc)(RaRm)
(Rb Rc )(I2 -Im) Im(Ra Rm) Since, Ra Rsh
(Rb Rc), yield, I2 (Rb Rc ) Im(RbRc)
Im Rsh (Rb Rc ) Rm
Middle sensitive range
----(d)
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The Aryton Shunt (contd)
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The Aryton Shunt (contd)

• Substitute eqn (d) into eqn (e), yields

----(f)
Ra Rsh (RbRc)
----(g)
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Example 2 The Aryton Shunt
Calculate the value for Ra, Rb and Rc as shown,
given the value of internal resistance, Rm1kO
and full scale current of the moving coil 100
µA. The required range of current are I1
10 mA, I2 100 mA and I3 1A.
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Solution Ex2
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Ammeter Insertion Effect
Connect Ammeter
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Example 3 Ammeter Insertion Effects
A current meter that has an internal resistance
of 78O is used to measure the current through
resistor R1. Determine the percentage of error of
the reading due to ammeter insertion.
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Solution Ex3
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DC Voltmeter

• DMM become VOLTMETER multiplier Rs in series
  with the meter movement.

To extend the voltage range
PURPOSE
To limit current through the DMM to a maximum
full-scale deflection current
DMM DArsonval Meter Movement
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DC Voltmeter (contd)
Unit derivation
Ifs Im full scale deflection current
Rs Rm (S x Vrange)
It is desirable to make R(voltmeter) gtgtR (
circuit)
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Example 4 DC Voltmeter

• Calculate the value of the multiplier resistance
  on the 50 V range of a dc voltmeter that used a
  500µA dArsonval meter with an internal
  resistance of 1 kO.

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Solution Ex4
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Multi-Range Voltmeter

• A multi-range voltmeter consists of a deflection
  instrument, several multiplier resistors and a
  rotary switch.

only one of the three multiplier resistors is
connected in series with the meter at any time.
The range of this meter is
Where the multiplier resistance, R
can be R1 or R2 or R3
Multi-range Voltmeter
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Multi-Range Voltmeter (contd)
The multiplier resistors are connected in series,
and each junction is connected to one of the
switch terminals. The range of this voltmeter can
be also calculated from the equation
3V
10V
30V
Where the multiplier, R, now can be R1 or
(R1 R2) or (R1 R2 R3) (Note the largest
voltage range must be associated with the largest
sum of the multiplier resistance)
A commercial version of a multi-range voltmeter
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Example 5 multi-range Voltmeter
Calculate the value of the multiplier resistance
for the multiple range dc voltmeter circuit shown
in Figure (a) and Figure (b), if Ifs 50µA and
Rm 1k?
3V
10V
30V
Figure (a)
Figure (b)
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Solution Ex5
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Voltmeter Loading Effect
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Voltmeter Loading Effect (contd)

• Calculation
• 1)
• 2)
• 3)
• 4)
• 5)

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Example 6 Voltmeter Loading Effect
A volt meter (0-10V) that has an internal
resistance of 78O is used to measure the voltage
across resistor RB. Determine the percentage of
error of the reading due to voltmeter insertion.
Let E 4V, RARB 1kO , S 1kO/V
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Solution Ex6
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DC Ohmmeter

• Basic Ohmmeter circuit

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DC Ohmmeter (contd)
Before measuring the Rx, the Ometer is set to
zero-calibration
Definition zero shorting the terminal x-y
adjust Rz to obtain the full-scale
deflection on the meter movement.
w/o Rx
I lt Ifs
with Rx
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DC Ohmmeter (contd)

• Relationship between full-scale deflection to
  the value of Rx is

This equation is used for marking off the scale
on the meter face of the ohmmeter to indicate the
value of a resistor being measured
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Example 7DC Ohmmeter

• A 1 mA full-scale deflection current meter
  movement is to be used in an ohmmeter circuit.
  The meter movement has an internal resistance,
  Rm, of 100O, and a 3 V battery will be used in
  the circuit. If the measured resistor has
  resistance of 1kO, mark off the meter face for
  the reading (20, 40, 50, 75 and 100) .

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Solution Ex7
Ohm
Full scale percentage
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Multiple-range Ohmmeter
The previous section is not capable of measuring
resistance over wide range of values. We need to
extend our discussion of ohmmeters to include
multiple-range ohmmeters
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END OF PART 1