DC Voltmeters

Still in Chapter 02

Warm-ups

Stand-up. Take a deep breath 3x. Sit down and relax. Enjoy a short movie.

Warm-ups

Objectives

At the end of this lecture, students should be able to:

explain the purpose of multipliers put in series with a meter movements.

calculate the multiplier resistance of a Voltmeter.

explain and calculate the voltmeter loading effects.

DC Voltmeter Most D'Arsonval meter movements are

sensitive devices- have full-scale deflection current ratings as low as 50 µA, with an (internal) wire resistance of less than 1000 Ω.

This makes for a voltmeter with a full-scale rating of only 50 mV= (50 µA X 1000 Ω)!.

DC Voltmeter In order to build voltmeters with

practical scales from such sensitive movements, we need to reduce the voltage down to a level the movement can handle…

The basic d’Arsonval meter movement can be converted to a DC Voltmeter by connecting a Multiplier (Rs) with the meter movement.

DC Voltmeter

Rs

Rm

Im

+

-

Figure 1: The d’Arsonval meter movement used in a DC voltmeter

DC Voltmeter

The purposes of the Multiplier (Rs): to extend the voltage range of the

meter movements. to limit the current trough the

d’Arsonval meter movement to a maximum full-scale deflection current.

DC Voltmeter To find Rs value, we may first

determine the Sensitivity, S of the meter movements.

Sensitivity, S is the reciprocal? of the full-scale deflection current, as below:

)/(1

VI

Sfs

DC Voltmeter The units of sensitivity is Ohms per Volts.

)/(1

VI

Sfs

DC Voltmeter

Voltage measurements are made by placing the Voltmeter across the resistance of interest.

DC Voltmeter

This in effect places the total voltmeter resistances in parallel with the measured circuit resistance.

Therefore, it is desirable to make the voltmeter resistance much-much more higher than the circuit resistance.

DC Voltmeter

Since the value of the multiplier is different for each range, total resistance is difficult to express.

More meaningful info can be conveyed via Sensitivity rating of the instrument- telling the resistance of the instrument for a-one-volt range.

DC Voltmeter

To determine the total resistance (Rs+Rm)? that a voltmeter present to a circuit, just multiply the Sensitivity by the Range.

Thus; Rs +Rm = S X Range

Rs = S X Range – Rm

DC Voltmeter

Example 1. Calculate the sensitivity of a 100-A meter

movement which is to be used as a DC Voltmeter.

Example 2. 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 3. 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 4. 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

Summary

In this sub-topic, we have learned about:

the purpose of multipliers put in series with a meter movements.

calculation of the multiplier resistance of a Voltmeter.

voltmeter loading effects.

Conclusion The basic d’Arsonval meter movement can

be converted to a DC Voltmeter by connecting a Multiplier (Rs) with the meter movement.

Sensitivity, S is the reciprocal of the full-scale deflection current.

Therefore, it is desirable to make the voltmeter resistance much-much more higher than the circuit resistance.

Evaluation

Quiz 04