Chapter 5: DC Voltmeter



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).

1

V



I m R s



I m R m R s

 Given

1



V I m

V  

R m

Range

R s



1 I m



Range



R m

The the reciprocal current of full sensitivit scale y of the current meter   I 1   m 

R s



S



Range



R m

total voltmeter resistance 

S



Range

  is 2

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

R s



I V m



R m I m R s



100



μA 50 V 100 μA



1 k Ω



499 k Ω

3

At 0.8 FSD:

I V m

  

I 0.8

m 80



R



s μA 100



R m



499 μA



k Ω

 

80 1 μA k Ω

 

40 V

At 0.5 FSD:

I V m

 

50 50 μA μA



499 k Ω



1 k Ω

 

25 V

At 0.2 FSD:

I V m

 

20 20 μA μA



499 k Ω



1 k Ω

 

10 V

• The voltmeter designed in Example 5.1 has a total resistance of

R v = R s +R m = 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.

4

– Swamping Resistance

• The change in coil resistance (R m ) with temperature change can introduce errors in a PMMC voltmeter.

5

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

– 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 = I m (R m +R)

where R can be

R 1 , R 2 ,

or

R 3

6

• 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 = I m (R m +R)

where R can now be

R 1

,

R 1 +R 2

, or

R 1 +R 2 +R 3

.

• 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

R 1

special resistor.

is a 7

Example 5.2: A PMMC instrument with FSD = 50  A and R m = 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

Circuit as in Figure 3



16 R m



R 1 R 1

 

I V m I V m

 

10 V 50 μA R m



1700 Ω



198.3

k Ω R

2

R

3   50

V

50 

A

 998

.

3

k

 1700   100

V

50 

A

 1700  1

.

9983

M

  8

Circuit as in Figure 3  16 R m  R 1  V 1 I m R 1  V 1 I m  R m  10 V 50 μA  1700 Ω  198.3

kΩ R m  R 1  R 2  V 2 I m R 2  V 2 I m  R 1  R m  50 V 50 μA  198.3

kΩ  1700 Ω  800 kΩ 9

R m  R 1  R 2  R 3  V 3 I m R 3  V 3 I m  R 2  R 1  R m  100 V 50 μA  800 kΩ  198.3

kΩ  1700 Ω  1 MΩ – Voltmeter Internal Resistance: R in

V R in

  

I S R s m R in

 

R m I



m



R I 1 m s

 

V R m



Range

 10

Example 5.3: From Example 5.2, Calculate R in for each range Solution Find sensitivity

S



1 I FSD



50 1 μA



20 k Ω V

Range V1 = 10V

R in



20 k Ω V



10 V



200 k Ω

Range V2 = 50V

R in



20 k Ω V



50 V



1 M Ω

Range V3 = 100V

R in



20 k Ω V



100 V



2 M Ω

11

– Voltmeter Loading Effect dc circuit with source and resistors Vwom Vth Rth Vwom dc circuit with source and resistors V Vwm Vth Rth V Vwm 12

Accuracy % % % V wom V wm Acc Acc Error



V Th

 

R in V



Th R Th V wm V wom

 

R in R in R



in R Th

 

V wm V wom



100% R in R



in R Th



100%



1



% Acc



X t



X t X m



V wom



V wom V wm



100%



100%

13

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 Find

V Th

,

R Th

,

R in V Th



V wom

  

R

1

E



R

2  

R

2

R Th

 

R

1 200

k

100

V

  200

k

 //

R

2  200

k

 //  200

k

  50 200

k

  100

k

 14

R in



S



Range

 20

k

  50

V V

 1

M

 Find reading voltage,

V wm

or

V wm

  

R in R in



R Th

  

V wom

1

M

 1

M

  100

k

  50

V

 45 .

45

V V wm

  

R in V Th



R Th

 

R in

 1

M

 50

V

 100

k

  1

M

Find accuracy of measuremen t   45 .

45

V

or

Accuracy



V wm V wom

 45 .

45 50

V V

0 .

909

Accuracy

 

R in R



in R Th

1

M

 1

M

  200

k

  0 .

909 15

Find error of measuremen t or

Error Error

 1 

Acc

 1  0 .

909  0 .

091 

X t



X m X t

 50

V

 45 .

45

V

50

V

 0 .

091 16