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Transcript
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 Rs I m Rm Rs 1 V Rm Im Given V Range 1 Rs Range Rm Im 1 The reciprocal of full scale current Im the current sensitivit y of the meter S Rs S Range Rm 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 V Rs Rm Im I m 100 μA 50 V Rs 1 kΩ 499 kΩ 100 μA 3 At 0.8 FSD: I m 0.8 100 μA 80 μA V I m R s R m 80 μA 499 kΩ 1 kΩ 40 V At 0.5 FSD: I m 50 μA V 50 μA 499 kΩ 1 kΩ 25 V At 0.2 FSD: I m 20 μA V 20 μA 499 kΩ 1 kΩ 10 V • 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. 4 – Swamping Resistance • The change in coil resistance (Rm) with temperature change can introduce errors in a PMMC voltmeter. 5 • 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 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 = 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. 7 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 Circuit as in Figure 3 16 a R m R1 R1 V Im V Rm Im 10 V 1700 Ω 50 μA 198.3 kΩ R2 50 V 1700 50 A 998 . 3 k 100 V R3 1700 50 A 1 . 9983 M 8 Circuit as in Figure 3 16b V1 R m R1 Im V1 R1 Rm Im 10 V 1700 Ω 50 μA 198.3 kΩ V2 R m R1 R 2 Im R2 V2 R1 R m Im 50 V 198.3 kΩ 1700 Ω 50 μA 800 kΩ 9 V3 R m R1 R 2 R 3 Im R3 V3 R 2 R1 R m Im 100 V 800 kΩ 198.3 kΩ 1700 Ω 50 μA 1 MΩ – Voltmeter Internal Resistance: Rin V I m R in I m R s R m R in R s R m 1 V Im S Range 10 Example 5.3: From Example 5.2, Calculate Rin for each range Solution Find sensitivity S 1 I FSD 1 kΩ 20 50 μA V Range V1 = 10V kΩ R in 20 10 V 200 kΩ V Range V2 = 50V R in 20 kΩ 50 V 1 MΩ V Range V3 = 100V R in 20 kΩ 100 V 2 MΩ V 11 – Voltmeter Loading Effect Rth dc circuit with source and resistors Vwom Vwom Vth Rth dc circuit with source and resistors V Vwm Vth V Vwm 12 Vwom VTh Vwm VTh R in R in RTh Vwm R in Accuracy Vwom R in RTh % Acc Vwm 100% Vwom % Acc R in 100% R in RTh % Error 1 % Acc Xt Xm 100% Xt Vwom Vwm 100% Vwom 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 VTh , RTh , Rin E R2 VTh Vwom R1 R2 100V 200k 50 200k 200k RTh R1 // R2 200k // 200k 100k 14 Rin S Range 20k 50V 1M V Find reading voltage, Vwm Rin Vwom Vwm Rin RTh 1M 50V 45.45V 1M 100k VTh Rin or Vwm Rin RTh 50V 1M 45.45V 1 M 100 k Find accuracy of measuremen t Vwm 45.45V Accuracy 0.909 Vwom 50V Rin or Accuracy Rin RTh 1M 0.909 1M 200k 15 Find error of measuremen t Error 1 Acc 1 0.909 0.091 X X m 50V 45.45V or Error t 0.091 Xt 50V 16