1. DC V OLTMETER ( CONT.) The basic d’arsonval meter movement can be converted to a dc voltmeter by connecting a multiplier (series resistance) R s in series with the meter movement as shown in fig. The multiplier limits the current through the movement so as not to exceed the value of the full-scale deflection current Im. - + RsRs RmRm ImIm

2. The value of a multiplier required to extend the voltage range is calculated as :- Where V = Full range voltage of the instrument. I m = Full scale deflection current. R m = Internal resistance of the moving coil. Rs = Multiplier resistance. DC V OLTMETER ( CONT.)

3. The multiplier is usually mounted inside the case of the voltmeter for moderate range up to 500v. But for higher voltage ranges, due to the excessive heating, inside the case, the multiplier is mounted outside the case.

4. M ULTI - RANGE V OLTMETER Not Practical. - R1R1 R2R2 R3R3 R4R4 V1V1 V2V2 V3V3 V4V4 + RmRm ImIm

5. M ULTI - RANGE V OLTMETER Practical implementation. RmRm ImIm + V4V4 R1R1 R2R2 R3R3 R4R4 V3V3 V2V2 V1V1

6. V OLTMETER S ENSITIVITY The voltmeter sensitivity (S) is defined as The reciprocal of the full scale deflection The multiplier resistance R s is given by i.e

7. L OADING E FFECT The sensitivity of a dc voltmeter is an important factor when selecting a meter for measuring certain voltage. A low sensitivity meter may give correct reading when measuring voltage in low resistance circuit. For high resistance circuits it produce unreliable reading because the voltmeter represents a shunt resistance to the circuit resistance thus reduce the equivalent resistance of the circuit and the meter will give a lower indication of the voltage drop than the actual one.

8. E XAMPLE Ex: It is desired to measure the voltage across the 50 kΩ resistor shown in the fig. Two voltmeter of Sensitivity 1000 Ω/v and 20000 Ω/v are used. Both meter are used on their 50 v range. Calculate:- i- The reading of each voltmeter. ii-The error in each reading expressed as a percentage of the true value.

9. E XAMPLE ( CONT.) v b a 50 kΩ 100 KΩ 150 v _ +

10. E XAMPLE ( CONT.) (a) The voltage across the resistor 50 kΩ is Using voltmeter (a): S = 1000 Ω/v R T = S. V = 50 * 1000 = 50 kΩ: Thus the equivalent resistance between points a, b is 25 kΩ Thus the reading of the voltmeter =

11. E XAMPLE ( CONT.) Using voltmeter (b): S = 20000 Ω/v. R T = S. V = 50 * 20000 = 1 MΩ. The equivalent resistance between the point a, b is : Thus V 2 = which is indicated on the voltmeter.

12. E XAMPLE ( CONT.) The error: = ((50 – 30)/50) * 100% = 40% in 1 st case in second case: error = ((50 – 48.36)/50) * 100% = 3.28%

13. P RECAUTION FOR MEASURING VOLT : i) Correct polarities. ii) Putting across R. iii) First use the biggest range and then reduce it. iv) Be-aware with the loading effect. V

14. P RECAUTION FOR MEASURING VOLT : EX: DC voltmeter, R m = 100 Ω, I fsd = I m = 1mA, voltage range are 0-10 v, 0-50 v, 0-250 v, 0-500 v Calculate the multipliers R 4, R 3, R 2, R 1 as shown in fig.3. Solution: For range 0-10 v: R T = S. V = V/I m = 10/(1*10 -3 ) = 10 k Ω R T = R 4 + R m = R 4 + 100 R 4 = R T – R m = 10*10 3 – 100 = 9.900 k Ω

15. P RECAUTION FOR MEASURING VOLT : For range 0-50 v: RT = S. V = V/Im = 50/(1*10-3) = 50 k Ω. RT = R3 + R4 + Rm. R3 = 50*103 – 10*103 = 40 k Ω. For range 0-100 v: RT = S. V = V/Im = 100/(1*10-3) = 100 k Ω. RT = R2 + R3 + R4 + Rm = R2 + 50*103. R2 = (100 – 50)103 = 50 k Ω.

16. P RECAUTION FOR MEASURING VOLT : For range 0-500 v: RT = S. V = V/Im = 500/(1*10-3) = 500 k Ω. RT = R1 + R2 + R3 + R4 + Rm = R1 + 100 k Ω. R1 = 400 k Ω.