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CHAPTER 2 : DC METER
2.1.1 PMMC
The Permanent Magnet Moving Coil (PMMC) galvanometer used for dc measurement only.
The motor action is produced by the flow of a small current throught a moving coil which is positioned in the field of a permanent magnet
The basic moving coil system-D’Arsonval galvonometer
Figure 2.1: d’Arsonval meter
2.1.3 Deflecting Torque
Resulting from the effects of magnetic electrostatic.
This torque causes the pointer moves from the zero position
IRON CORE
SN
F
F
DEFLECTING TORQUE
Td = BANI (Nm) B = flux density in Wb/m2 or Tesla (T)
N = number of coils
A = Area cross-section
(length (l) x coil diameter (d)m2 )
I = current flowing through the coil - Ampere
2.1.4 DAMPING CURVE
Works to speed up the pointer stops Pointer may oscillate before the show
reading and damping torque required to accelerate the needle stops.
Damping curve
Steady state
0
Under damp
Critical damp
Over damp
t
V
2.1.5 Damping Curve
Over damp – pointer will move slowly and never reach the steady state. The value will be less than the actual value.
Under damp - pointer will oscillate until it finally reach
the final value. The result is difficult to read. Critical damp - pointer to achieve the true value of
free oscillations in a short time.
2.1.6 Types of damping
Eddy current dampingAir friction dampingFluid damping
EDDY CURRENT DAMPING
An aluminum disc D, is controlled by a reel, can be move between a the pole of a permanent magnet M.
If the disk moves clockwise, the e.m.f induced in the disc circulate eddy currents distribution as shown (interrupted lines). From Lenz Law, the current will impose a force against the movement of their forms. Therefore, the resulting damping force is counter clockwise.
MD
Air friction Damping
A piece of the blade is attached to the moving parts in the meter. Resistance produced by the air around will give the desired damping.
Fluid damping
The same principle is used but the blade is allowed to move in a container of liquid with suitable viscosity.
2.2 DC VOLTMETER
The basic d’Arsonval meter can be converted to a dc voltmeter by connecting a multiplier Rs in series with it as shown in Figure 2.6. The purpose of the multiplier is to extend the range of the meter and to limit the current through the d’Arsonval meter to the maximum full-scale deflection current.
2.2.1 Basic DC Voltmeter circuit
To find the value of the multiplier resistor, we may first determine the sensitivity, S, of the d’Arsonval. If the sensitivity is known, the total voltmeter resistance can be calculated easily.The sensitivity of a voltmeter is always specified by the manufacturer, and is frequently printed on the scale of the instrument.
Figure 2.6
Voltmeter
• If the full-scale meter current is known, the sensitivity can be determined as the reciprocal of the full scale current.
Sensitivity = 1 / Ifs
Where Ifs is the full-scale deflection current of d’Arsonval meter.
2.2.2 Multiplier Resistance
The value of the multiplier resistance can be found using this relationship:
Rs + Rm = S x Vrange Thus,
Rs = (S x Vrange) - Rm
2.2.3 Example
Calculate the value of the multiplier resistance on the 50 V range of a dc voltmeter that used a 500μA d’Arsonval meter with an internal resistance of 1 kΩ.
Solution :
S = 1/Ifs
= 1/500µA = 2KΩ/V
Rs = S x Range – Rm
= 2 kΩ/V x 50 V – 1 kΩ
= 99 kΩ
2.2.4 Multi range Voltmeter
A multi range voltmeter consists of a deflection instrument, several multiplier resistors and a rotary switch. Two possible circuits are illustrated in Figure 2.7 (a) and (b).
Figure 2.7(a): Multirange Voltmeter
In figure 2.7 (a) only one of the three multiplier resistors is connected in series with the meter at any time. The range of this meter is
V = Im ( R + Rm )
Where the multiplier resistance, R can be R1 or R2 or R3.
Figure 2.7(b): A commercial version of a multi range voltmeter
In figure 2.7(b) 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
V = Im (Rm + R)
Where the multiplier, R, now can be R3 or (R3 + R2) or (R1 + R2 + R3) (Note: the largest voltage range must be associated with the largest sum of the multiplier resistance)
2.2.5 Example
Calculate the value of the multiplier resistance for the multiple range dc voltmeter circuit shown in Figure 2.7(a) and Figure 2.7(b), if Ifs = 50μA and Rm = 1kΩ
2.2.6
2.2.7 DC Voltmeter Loading Effect
As the DC ammeter, the DC voltmeter also observe for loading effect whenever it is inserted to a measured circuit. Figure 2.7 shows a circuit with the DC voltmeter is inserted into it. Inserting voltmeter always increase the resistance and decrease the current flowing through the circuit.
Figure 2.7: Circuit with voltmeter insertion effect
Without the insertion of the DC voltmeter, the voltage VRB can be found as:
VRB = _______ X E
RB + RA
RB
Inserting the voltmeter in parallel with RB gives us the total inserted resistance as :
RT = RS + RM
Thus, yield to
Req = RB //RT
2.2.8 LOADING EFFECT
Now, the voltage VRBm with the voltmeter
insertion is found as:
VRB = ________ x E
Req + RA
Req
Therefore,
Insertion error = VRB – VRBm
X 100%
VRB
DC Voltmeter
Example 1. Calculate the value of the multiplier Rs on
the 50-V range of a DC Voltmeter that used 200-A meter movements with an internal resistance of 1.2kΩ.
DC Voltmeter
Example 2. Calculate the
values of Rs for the multiple- range DC Voltmeter circuits as shown below:
Rs1
Rm = 2 kΩ
Ifs = 100A
+ -
Rs2 Rs3
5V 30V10V
DC Voltmeter
Example 3. Calculate the
values of Rs for the multiple- range DC Voltmeter circuits as shown below:
RcRm = 2 kΩ
Ifs = 50A
+ -
5V
50V
10V
RaRb
Voltmeter Loading Effects When a voltmeter is used to measure the
voltage across a circuit component, the voltmeter circuit itself is in parallel with the circuit component.
Since the parallel combination of two resistors is less than either resistor alone, the resistor seen by the source is less with the voltmeter connector than without.
Voltmeter Loading Effects
Therefore, the voltage across the component is less whenever the voltmeter is connected.
The decrease in voltage maybe negligible or appreciable, depending on the Sensitivity of the voltmeter being used.
This effect is called voltmeter loading and the resulting error is called loading error.
Voltmeter Loading EffectsExample 5: Two different voltmeters are used to
measure the voltage across RB in the circuit below. The meters are:
Meter A : S= 1kΩ/V;Rm=0.2kΩ; Range =10VMeter B : S=20kΩ/V;Rm=2.2kΩ; Range = 10V
Calculate: Voltage across RB without any
meter. Voltage across RB when meter A is
used. Voltage across RB when meter B is
used. Loading Errors in both voltmeter
readings.
RB
E = 20V
RA 10kΩ
1.8kΩ
Voltmeter Loading EffectsExample 6: Find the voltage reading and the
percentage of loading error of each reading obtained with a voltmeter on: Its 5-V range. Its 10-V range Its 50-V range.The meter has a 20-kΩ/V
sensitivity and connected across RA.
RB
E = 20V
RA 2.2kΩ
8.2kΩ