59 connection of a voltmeter and an ammeter to an

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Unformatted text preview: ing + Voltmeter V V − pointer Element S permanent magnet N spring rotating coil Figure 2.59 Connection of a voltmeter and an ammeter to an element. stationary iron core | v v Figure 2.58 | A d’Arsonval meter movement. e-Text Main Menu | Textbook Table of Contents | Problem Solving Workbook Contents 58 PART 1 DC Circuits Meter Multiplier Rn + Probes Im Rm V − (a) R1 1V R2 + 100 V R3 Probes V − Meter Switch 10 V Im Rm (b) Figure 2.60 Voltmeters: (a) single-range type, (b) multiple-range type. Rn In internal resistance Rm , Meter Im Vfs = Ifs (Rn + Rm ) Rm From this, we obtain I Probes Rn = (a) 10 mA R2 100 mA Switch 1A R3 Meter Im Rm I Probes (b) Ammeters: (a) single-range type, (b) multiple-range type. v v Figure 2.61 | e-Text Main Menu Vfs − Rm Ifs (2.60) Similarly, the ammeter measures the current through the load and is connected in series with it. As shown in Fig. 2.61(a), the ammeter consists of a d’Arsonval movement in parallel with a resistor whose resistance Rm is deliberately made very small (theoretically, zero) to minimize the voltage drop across it. To allow multiple range, shunt resistors are often connected in parallel with Rm as shown in Fig. 2.61(b). The shunt resistors allow the meter to measure in the range 0 –10 mA, 0 –100 mA, or 0 –1 A, depending on whether the switch is connected to R1 , R2 , or R3 , respectively. Now our objective is to obtain the multiplier shunt Rn for the singlerange ammeter in Fig. 2.61(a), or Rn = R1 , R2 , or R3 for the multiplerange ammeter in Fig. 2.61(b). We notice that Rm and Rn are in parallel and that at full-scale reading I = Ifs = Im + In , where In is the current through the shunt resistor Rn . Applying the current division principle yields R1 | (2.59) Im = | Textbook Table of Contents | Rn Ifs Rn + R m Problem Solving Workbook Contents CHAPTER 2 Basic Laws 59 or Im Rm (2.61) Ifs − Im The resistance Rx of a linear resistor can be measured in two ways. An indirect way is to measure the current I that flows through it by connecting an ammeter in series with it and the voltage V across it by conn...
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