Here are the key details about the voltmeter and circuit: - Voltmeter has sensitivities of 20 kΩ/V - It has ranges of 5 V, 10 V, and 50 V - It is connected across resistor RA in the circuit The question is asking to calculate: 1) The voltage reading on the 5 V range 2) The voltage reading on the 10 V range 3) The voltage reading on the 50 V range 4) The percentage loading error for each reading Given these details, the appropriate calculations using the voltmeter loading effects equations can be done to solve the problem.

1. CHAPTER 2 : DC METER

2. 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

3. Figure 2.1: d’Arsonval meter

4. 2.1.3 Deflecting Torque
 Resulting from the effects of magnetic
electrostatic.
 This torque causes the pointer moves from
the zero position
F
IRON CORE
N S
F

5. 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

6. 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.

7. Damping curve
V
Under damp
Critical damp
Steady
state
Over damp
t
0

8. 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.

9. 2.1.6 Types of damping
Eddy current damping
Air friction damping
Fluid damping

10. 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.
M
D

11. 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.

12. Fluid damping
 The same principle is used but the blade is
allowed to move in a container of liquid with
suitable viscosity.

13. 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.

14. 2.2.1 Basic DC Voltmeter circuit
Figure 2.6
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.

15. 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.

16. 2.2.2 Multiplier Resistance
 Thevalue of the multiplier resistance can be
found using this relationship:
Rs + Rm = S x Vrange
 Thus,
Rs = (S x Vrange) - Rm

17. 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.

18. Solution :
 S = 1/Ifs
= 1/500µA = 2KΩ/V
Rs = S x Range – Rm
= 2 kΩ/V x 50 V – 1 kΩ
= 99 kΩ

19. 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

20.  Infigure 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.

21. Figure 2.7(b): A commercial version of a multi range voltmeter

22.  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)

23. 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

24. 2.2.6

25. 2.2.7
DC Voltmeter Loading Effect
 Asthe 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.

26. Figure 2.7: Circuit with voltmeter insertion effect

27.  Withoutthe insertion of the DC voltmeter, the
voltage VRB can be found as:
RB
VRB = _______ X E
RB + RA

28. 2.2.8 LOADING EFFECT
 Inserting the voltmeter in parallel with RB
gives us the total inserted resistance as :
RT = RS + RM
 Thus, yield to
Req = RB //RT

29. m
 Now, the voltage VRB with the voltmeter
insertion is found as:
Req
VRB = ________ x E
Req + RA

30.  Therefore,
m
Insertion error = VRB – VRB X 100%
VRB

32. DC Voltmeter
Example 1.
 Calculate the value of the multiplier Rs on
the 50-V range of a DC Voltmeter that used
200-µA meter movements with an internal
resistance of 1.2kΩ.

33. DC Voltmeter
Example 2.
 Calculate the
values of Rs for
the multiple-
range DC
Voltmeter
circuits as
shown below:

34. DC Voltmeter
Example 3.
 Calculate the
values of Rs for
the multiple-
range DC
Voltmeter
circuits as
shown below:

35. 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.

36. 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.

37. Voltmeter Loading Effects
Example 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 =10V
Meter 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.

38. Voltmeter Loading Effects
Example 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.