1

Voltmeter Circuit– Extremely high resistance

– Always connected across or in parallel with the points in a circuit at which the voltage is to be measured

– The voltmeter range is increased by connecting a multiplier resistance with the instrument (single or individual type of extension of range).

Chapter 5: DC Voltmeter

2

RangeS

RRangeSR

RRangeI

1R

RVI

1R

RIRIV

ms

mm

s

mm

s

mmsm

resistancevoltmetertotal

Smetertheofysensitivitcurrentthe

isI

1currentscalefullofreciprocalThe

RangeVGiven

m

3

Example 5.1: A PMMC instrument with FSD of 100 A and a coil resistance of 1k is to be converted into a voltmeter. Determine the required multiplier resistance if the voltmeter is to measure 50V at full scale (Figure 3-15). Also calculate the applied voltage when the instrument indicate 0.8, 0.5, and 0.2 of FSD.

Solution

For V=50V FSD

mm

s RI

VR

kΩ499kΩ1μA100

V50R

μA100I

s

m

4

At 0.8 FSD:

At 0.5 FSD:

At 0.2 FSD:

• The voltmeter designed in Example 5.1 has a total resistance of Rv = Rs+Rm = 500k . Since the instrument measures 50V at full scale, its resistance per volt or sensitivity is 500k / 50V =10 k / V.

• The sensitivity of a voltmeter is always specified by the manufacturer, and it is frequently printed on the scale of the instrument.

V40kΩ1kΩ499μA80

RRIV

μA80μA1000.8I

msm

m

V25kΩ1kΩ499μA50V

μA50I m

V10kΩ1kΩ499μA20V

μA20I m

5

– Swamping Resistance• The change in coil resistance (Rm)

with temperature change can introduce errors in a PMMC voltmeter.

6

• The presence of the voltmeter multiplier resistance (Rs) tends to swamp coil resistance changes, except for low voltage ranges where Rx is not very much larger than Rm.

– Multi-range Voltmeter• In Figure 3.16(a), only one of the

three multiplier resistors is connected in series with the meter at any time.

• The range of this voltmeter is

V = Im(Rm+R)

where R can be R1, R2, or R3

7

• In Figure 3.16(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 also be calculated from the equation

V = Im(Rm+R)

where R can now be R1, R1+R2, or R1+R2 +R3.

• Of the two circuits, the on in Figure 3.16(b) is the least expensive to construct. This is because all of the multiplier resistors in Figure 3.16(a) must be special (nonstandard) values, while in Figure 3.16(b) only R1 is a special resistor.

8

Example 5.2: A PMMC instrument with FSD = 50A and Rm = 1700 is to be employed as a voltmeter with ranges of 10V, 50V, and 100V. Calculate the required values of multiplier resistors for the circuits of Figure 3.16(a) and (b).

Solution

kΩ198.3

Ω1700μA50

V10

RI

VR

I

VRR

a163FigureinasCircuit

mm

1

m1m

M.

A

VR

k.

A

VR

99831

170050

100

3998

170050

50

3

2

9

kΩ800

Ω1700kΩ198.3μA50

V50

RRI

VR

I

VRRR

kΩ198.3

Ω1700μA50

V10

RI

VR

I

VRR

b163FigureinasCircuit

m1m

22

m

221m

mm

11

m

11m

10

– Voltmeter Internal Resistance: Rin

RangeS

VI

1RRR

RRIRIV

mmsin

msminm

MΩ1

Ω1700kΩ198.3kΩ800μA50

V100

RRRI

VR

I

VRRRR

m12m

33

m

3321m

11

Example 5.3: From Example 5.2, Calculate Rin for each range

Solution

Find sensitivity

Range V1 = 10V

Range V2 = 50V

Range V3 = 100V

V

kΩ20

μA50

1

I

1S

FSD

kΩ200V10V

kΩ20R in

MΩ1V50V

kΩ20R in

MΩ2V100V

kΩ20R in

12

– Voltmeter Loading Effect

R th

Vthdc circuit with source

and resistors Vwom

R th

Vthdc circuit with source

and resistorsVwmVwmV V

Vwom

13

100%V

VV

100%X

XXAcc%1Error%

100%RR

RAcc%

100%V

VAcc%

RR

R

V

VAccuracy

RRR

VV

VV

wom

wmwom

t

mt

Thin

in

wom

wm

Thin

in

wom

wm

inThin

Thwm

Thwom

14

Example 5.4 A voltmeter with sensitivity of 20kΩ/V is used for measuring a voltage across R2 with range of 50V as shown in figure below. Calculate

a) reading voltage

b) accuracy of measurement

c) error of measurement

Solution

inThTh RRV ,,Find

kkkRRR

kkk

V

RRR

EVV

Th

womTh

100200//200//

50200200200

100

21

221

15

MVV

kRangeSRin 150

20

wmVvoltage,readingFind

VVkM

M

VRR

RV wom

Thin

inwm

45.45501001

1

VMkM

V

RRR

VV in

Thin

Thwm

45.4511001

50

or

tmeasuremenofaccuracyFind

909.050

45.45V

VV

VAccuracy

wom

wm

909.02001

1

or

kMM

RR

RAccuracy

Thin

in

16

tmeasuremenoferrorFind

091.050

45.4550or

091.0909.011

VVV

X

XXError

AccError

t

mt