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<\/p>\nThere are two methods of calculating the values of multiplier resistors for a multirange voltmeter. In the first method, each multiplier is calculated the same as for a single-range voltmeter. Assume that you wish to extend the range of a 1-mA movement to measure 0- 10, 0- 100, and 0- 1000 volts, and you also want a 0- 1-V range. Since full-scale deflection equals 1 Von the 0- 1-V range (V = IM RM = 0.001 A x 1000 Q = I volt), no multiplier is needed. The total resistance (RT OT) needed to limit meter current (IM) to 1 mA on the 0- 10-V range is RrnT = V w vJ IM\u00a0\u00a0 =\u00a0\u00a0 10 V\/ 0.001A=\u00a0\u00a0\u00a0 10,000 Q<\/p>\n
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Since the resistance of the meter (RM) is 1000 ohms, then the multiplier resistance RMuLT is 9000 ohms. A second method of calculating the values of voltmeter multiplier resistors is the series-multiplier arrangement in which the multiplier resistors are connected in series. R1 is the multiplier resistor for the 0-10 volt range. For the 0- 100-V range, R1 is in series with R2. Therefore, the value of the multiplier resistance for the 0- 100-V range is equal to R1 plus R2. Similarly, the multiplier resistance for the 0-1000-V range is equal to R1 plus R2 plus R3.<\/p>\n
Now, let\u2019s calculate the values for a series multiplier voltmeter. We will use the same 1-mA, 1000-Q meter movement that we used previously. Since this movement indicates 1 volt for a full-scale deflection, no multiplier resistor is needed for the 0- 1-V range. Therefore, your first step is to calculate the multiplier resistance needed for the 0- 10-V range. Again, using Ohm\u2019s law, find the total resistance (RToT) needed to limit meter current (IM) to 1 mA at this range:<\/p>\n
RrnT = V w.xl lM\u00a0\u00a0\u00a0\u00a0 = 10 V\/ 0.001 A = 10,000 Q<\/p>\n
Therefore, multiplier resistor R1 for the 0-10-V range equals 10,000n minus the 1000-Qmeter resistance, or 9000 n. Thus far, the procedure is the same as in the other method, and the value of the multiplier resistor is the same for the 0- 10-V range. Having found the series multipliers for the 0- 1- and 0- 10-V ranges, let\u2019s calculate the total resistance needed for the 0- 100-Vrange:<\/p>\n
RrnT = vM AXl\u2019IM = 100 v; o.001 A = 100,000 n<\/p>\n
Subtracting the meter resistance from the total resistance, you find that the multiplier resistance for the 0- 100-V range is 99,000 ohms. Thus far, this method is the same as the previous, but now the multiplier resistance is made up of R I plus R2 in series. Therefore, since you need 99,000 n for the multiplier resistance and R I equal s 9000 n, R2 must equal 90,000 n.<\/p>\n
Similarly, for the 0-1000-V range:<\/p>\n
RT oT = VMNJ\u2019IM = 1000 v; o.001 A = 1,000,000 n<\/p>\n
Thus, RMuLT = RToT \u2013\u00a0\u00a0 RM = 1,000,000 \u2013\u00a0\u00a0 1000 = 999,000 n. But RMuLT = R1\u00a0\u00a0\u00a0 + R2\u00a0\u00a0 + R3.<\/p>\n
Thus, RMuLT =\u00a0\u00a0 999,000 n =\u00a0\u00a0 9000 + 90,000 + R3<\/p>\n
And R3 =\u00a0\u00a0 999,000 \u2013\u00a0\u00a0 99,000 =\u00a0\u00a0 900,000 n<\/p>\n
No matter which method you use, the value of the multiplier resistance for each range remains the same. However, in the first method, the multiplier is a single resistor, while in the second method, on all but the first extended range, it is made up of resistors in series.<\/p>\n
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References<\/p>\n
https:\/\/www.allaboutcircuits.com\/textbook\/direct-current\/chpt-8\/voltmeter-design\/<\/a><\/p>\n http:\/\/sound.whsites.net\/articles\/meters.htm<\/a><\/p>\n