2 dc meter

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