{"id":357,"date":"2018-11-29T11:24:54","date_gmt":"2018-11-29T11:24:54","guid":{"rendered":"http:\/\/msp04.epgpbooks.inflibnet.ac.in\/?post_type=chapter&p=357"},"modified":"2019-05-01T05:44:26","modified_gmt":"2019-05-01T05:44:26","slug":"analog-ammeters-and-voltmeters-ii","status":"publish","type":"chapter","link":"https:\/\/ebooks.inflibnet.ac.in\/msp04\/chapter\/analog-ammeters-and-voltmeters-ii\/","title":{"rendered":"Analog Ammeters and Voltmeters II"},"content":{"raw":"
\"epgp<\/a>\r\n<\/span><\/div>\r\n
\r\n\r\n\u00a0 \u00a0 Ammeter Shunts:<\/strong>\r\n\r\n \r\n\r\n \r\n

The basic movement of a d.c. ammeter is a PMMC d'Arsonva galvanometer. The coil winding of a basic movement is small and light and can carry very small currents since the construction of an accurate Instrument with a moving coil to carry currents greater than 100 mA is impracticable owing to the bulk anq weight of the coil that would be required. When heavy currents are to be measured, the major part of the current is bypassed through a low resistance called a \"shunt\". Fig. 1 shows the basic movement (meter) and its shunt to produce an ammeter.<\/em> The resistance of the shunt can be calculated using conventional circuit analysis.<\/p>\r\n \r\n\r\n\"\"\r\n\r\n \r\n

where R<\/em>m<\/em>=<\/em> internal resistance of movement (i.e.<\/em> the coil), Im = Ifs = full scale deflection current of movement, Rsh=resistance of the shunt, Ish=shunt current, I=current to be measured.<\/p>\r\n \r\n

Since the shunt resistance is in parallel with the meter movement, the voltage drops across shunt and movement must be the same.<\/p>\r\n \r\n\r\nor\u00a0\u00a0\u00a0 Ish Rsh =Im Rm\r\n\r\n \r\n\r\nThus, Rsh =Im Rm\/ Ish\r\n\r\n \r\n\r\nBut, Ish = I - Im\r\n\r\n \r\n\r\nTherefore, Rsh =Im Rm\/ (I- Im)\r\n\r\n \r\n\r\nSimplifying we get,\u00a0\u00a0\u00a0\u00a0 I\/Im = 1+ Rm\/Rsh\r\n\r\n \r\n\r\nThis ratio of total current to the current in the movement is called Multiplying power of shunt.\r\n\r\n \r\n\r\nMultiplying power,\u00a0 m = I\/Im = 1+ Rm\/Rsh\r\n\r\n \r\n\r\nResistance of shunt\u00a0\u00a0\u00a0 Rsh = Rm\/ (m-1)\r\n\r\n \r\n

The shunt resistance used with a d' Arsonval movement may consist of a coil of resistance wire within the case of the Instrument, or it may be external shunt having a very low resistance.<\/span><\/p>\r\n\r\n<\/div>\r\n

\r\n\r\n \r\n\r\nConstruction of Shunts:<\/strong>\r\n\r\n \r\n\r\nThe general requirements for shunts are:\r\n\r\n \r\n

(i)\u00a0 the temperature co-efficient of shunt and instrument should be low and should be as nearly as possible the same;<\/p>\r\n \r\n\r\n(ii) the resistance of shunts should not vary with time;\r\n\r\n \r\n\r\n(iii)\u00a0 they should carry the current without excessive temperature rise;\r\n\r\n \r\n\r\n(iv)\u00a0 <\/em>they should have a low thermal electromotive force.\r\n\r\n \r\n

'Manganin' is usually used for shunts of d.c. instruments as it gives low value of thermal emf with copper although it is liable to corrosion and is difficult to solder. 'Constantan' is a useful material for a c. circuits since its comparatively high thermal emf, being unidirectional, is ineffective on these circuits.<\/p>\r\n \r\n

The construction of shunts is the same as that of low resistance standards. Shunts for low currents are enclosed in the meter casing but for currents above 200 A they are mounted separately.<\/p>\r\n \r\n

Shunts for heavy currents are mounted externally. Fig 2 shows an external shunt. It consists of evenly spaced sheets of resistive material welded into large blocks of heavy copper on each end of sheets. The resistance material has a very low temperature co-efficient and a low thermal electric effect between the resistance material and the copper. The heavy lugs (current terminals) on each end of the shunt carry the load current while the binding posts (potential terminals) on each end of the shunt are used to connect the ammeter to the shunt and carry only the current which passes through the meter (movement).<\/p>\r\n \r\n\r\n\"\"\r\n\r\n \r\n

Fig. 2 Shunt for heavy currents<\/p>\r\n \r\n

Meters using external shunts are usually designed to operate at a full scale voltage rating. These ratings are usually 50, 75 or 100 m V. This is the voltage across the potential terminals of the shunt when full scale current\u00a0flows through the load. Inasmuch as the current producing the meter deflection is a function of the voltage drop across the potential terminals of the shunt and the resistance of the instrument including the leads, the meter used with external shunts must have leads with a specified resistance to accompany the meter. Leads supplied with the instrument should never be changed and also no portion of the leads should be cut off otherwise it will lead to serious calibration errors.<\/span><\/p>\r\n \r\n

Arrangement for Temperature Effect Correction:<\/strong><\/p>\r\n \r\n

The temperature error can be eliminated when the shunt and the moving-coil are made of the same material and kept at the same temperature. This method, however, is not satisfactory in practice as the temperatures of the two parts are not likely to change at the same rate. An additional disadvantage of using copper shunts is that they are likely to be bulky as the resistivity of copper is small. Copper shunts are only occasionally used in instruments with built-in shunts.<\/span><\/p>\r\n\r\n<\/div>\r\n

\r\n\r\n\"\"\r\n\r\n \r\n

Fig. 3 : Meter shunt and swamp resistance<\/p>\r\n \r\n

The arrangement normally used is shown in the Fig.3. In this case, \u2018swamping\u2019 resistance of Manganin having a resistance 20 to 30 times the coil resistance is connected in series with the coil and a shunt of Manganin is connected cross this combination. Since copper forms a small fraction of the series combination, the proportion in which the currents would divide between the meter and the shunt would not change appreciably with the change in temperature.<\/p>\r\n \r\n\r\nMulti-range Ammeters:<\/strong>\r\n\r\n \r\n

The current range of a d.c. ammeter may be further extended by a number of shunts, selected by a range switch. Such meter is called a multirange ammeter. Fig.4 shows a schematic diagram of multirange ammeter. The circuit has four shunts R<\/em>sh1<\/em> , R<\/em>sh2<\/em> , R<\/em>sh3<\/em> and R<\/em>sh4<\/em>,<\/em> which can be put in parallel with the meter movement to give four different current ranges I1, I2, I3 and I4.<\/p>\r\n\r\n<\/div>\r\n\"\"\r\n\r\n \r\n

Fig. 4: Multi range ammeter<\/span><\/p>\r\n\r\n

\r\n\r\n \r\n

Low range ammeters use a multiposition make before break switch (See in Fig. 4) provided on the case of the instrument. This type of switch is essential in order that the meter movement is not damaged when changing from the current range to another. If we provide an ordinary switch, the meter ramains without a shunt and as<\/em> such it is unprotected when the range is changed.<\/p>\r\n \r\n

When larger currents are used the connections are brought out to binding posts and the loads are connected directly to the binding post which is identified with the described current range. Multi-range ammeters are used for ranges from 1<\/em> to 50 A. When using a multi-range ammeter, first use the highest current range, then decrease the current range until good upscale reading is obtained.<\/p>\r\n \r\n

The universal shunt or Ayrton shunt is also used for multi-range ammeters. The advantage of an Ayrton shunt is that it eliminates the possibility of the meter being in the circuit without a shunt. But this advantage is gained at the cost of a higher meter resistance.<\/p>\r\n \r\n\r\nUniversal Shunt:<\/strong>\r\n\r\n \r\n\r\n\"\"\r\n\r\n \r\n

Fig. 5: Multi-range ammeter using universal shunt<\/p>\r\n \r\n

The universal shunt is presented here in a different form. Consider that the meter ranges have to be extended to I1, I2 and I3.<\/em> For the arrangement shown in Fig. 5, we have, for switch at position 1,<\/p>\r\n \r\n\r\nIm Rm = (I1 - Im) R1\r\n\r\n \r\n\r\nTherefore, m1 = I1 \/ Im = 1+ Rm\/R1\u00a0 or<\/strong> R1 = Rm\/(m1-1)\r\n\r\n \r\n\r\nFor switch at position 2, Im (R1 - R2 + Rm )= (I2 - Im) R2\u00a0<\/span>or R2 = (R1 + Rm)\/m2<\/span>\r\n\r\n \r\n\r\nFor switch at position 3, Im (R1 - R3 + Rm )= (I3 - Im) R3\u00a0<\/span>or R3 = (R1 + Rm)\/m3<\/span>\r\n\r\n \r\n\r\nThus the values of different selections of resistances <\/span>i.e.<\/em> (R1-R2), (R1- <\/span>R3),<\/em> and <\/span>R3<\/em> may be found.<\/span>\r\n\r\n<\/div>\r\n

\r\n\r\n \r\n\r\nVoltmeter Multipliers<\/strong>\r\n\r\n \r\n

A d'Arsonval basic meter movement is converted into a voltmeter by connecting a series resistance with it. This series resistance is known as a multiplier. The combination of the meter movement and the multiplier is put across the circuit whose voltage is to be measured.<\/p>\r\n \r\n\r\n\"\"\r\n\r\n \r\n

Fig. 6: Meter with a multiplier<\/p>\r\n \r\n

The multiplier limits the current through the meter so that it does not exceed the value for full scale deflection and thus prevents the movement form being damaged.<\/p>\r\n \r\n\r\nThe value of a multiplier, required to extend the voltage range, is calculated as under:\r\n\r\n \r\n\r\nLet\r\n\r\n \r\n\r\nl<\/em>m<\/em>=l<\/em>fs<\/em>=full <\/em>scale deflection current of meter,\r\n\r\n \r\n\r\nRm = internal resistance of meter movement,\r\n\r\n \r\n\r\nR<\/em>s<\/em> = multiplier resistance,\r\n\r\n \r\n\r\nv <\/em>= voltage across the meter movement for current I<\/em>m<\/em>,<\/em>\r\n\r\n \r\n\r\nV=fulI range voltage of instrument.\r\n\r\n \r\n\r\nFor the circuit of Fig. 6, v=l<\/em>m<\/em> R<\/em>m<\/em>\r\n\r\n \r\n\r\nV=l<\/em>m<\/em>(R<\/em>m<\/em>+ <\/em>Rs)\r\n\r\n \r\n\r\nTherefore, Rs = (V - l<\/em>m<\/em>R<\/em>m<\/em> )\/ l<\/em>m<\/em>\r\n\r\n \r\n\r\nWe can also express the result in terms of multiplying factor of multiplier.<\/span>\r\n\r\n \r\n\r\nMultiplying factor for multiplier, m = V\/<\/span>v = 1 + Rs\/Rm<\/em>\r\n\r\n \r\n\r\nThus, resistance of multiplier Rs = (m-1)Rm<\/span>\r\n\r\n \r\n

Hence for the measurement of voltage <\/span>m<\/em> times the voltage range of the instrument the series multiplying resistance should be (m-1) times the meter resistance. Thus to extend the voltage range to 10 times the instrument range, Rs =9 <\/span>Rm.<\/em><\/p>\r\n\r\n<\/div>\r\n

\r\n\r\n \r\n\r\nConstruction of Multipliers:<\/strong>\r\n\r\n \r\n\r\nThe essential requirements of multipliers are:\r\n\r\n \r\n\r\n(i)\u00a0 their resistance should not change with time;\r\n\r\n \r\n\r\n(ii) the change in their resistance with temperature should be small;\r\n\r\n \r\n\r\n(iii)\u00a0 they should be non-inductively wound for a.c. meters.\r\n\r\n \r\n\r\nThe resistance materials used for multipliers are manganin and constantan.\r\n\r\n \r\n

Multipliers are mounted inside the instrument case for voltages up to 500 V. For higher voltages, the multipliers may be mounted separately outside the case on a pair of binding posts to avoid excessive heating inside the case.<\/p>\r\n \r\n\r\nMultirange d.c. Voltmeters<\/strong>\r\n\r\n \r\n

In a multirange voltmeter, different full scale voltage ranges may be obtained by the use of individual multiplier resistors or by a potential divider arrangement.<\/p>\r\n \r\n

1.\u00a0lndividual Multipliers<\/strong>: We can obtain different voltage ranges by connecting different values of multiplier resistors in series with the meter. The number of these resistors is equal to the number of ranges required. Fig. 7 shows multiplier resistors R<\/em>s1<\/em>,<\/em> Rs2, R<\/em>s3<\/em> and R<\/em>s4<\/em> which can be connected in series with the meter by a range selector switch. Consider that the ranges desired are V1, V<\/em>2<\/em>, V<\/em>3<\/em> and V<\/em>4<\/em>,<\/em> then the corresponding multiplier resistances can be obtained.<\/p>\r\n \r\n\r\n\"\"\r\n\r\n<\/div>\r\n

\r\n

Fig. 7 : Multirange Voltmeter<\/p>\r\n \r\n\r\nThus, we have\r\n\r\n \r\n\r\nRs1 = (m1-1)Rm , Rs2 = (m2-1)Rm , Rs3 = (m3-1)Rm , Rs4 = (m4-1)Rm\r\n\r\n \r\n\r\n2. Potential Divider Arrangement:<\/strong>\r\n\r\n \r\n

Another multi-range voltmeter is shown in Fig. 8 in which the connections are made at the junctions of resistances R1. R2,<\/em> R3 and R4<\/em> in series to obtain the voltage range V1, V2,<\/em> V3 and V4.<\/em> These connections are brought out to binding posts on the instrument, and the instrument is connected to the proper binding post for the desired voltage range.<\/p>\r\n \r\n\r\n\"\"\r\n\r\n \r\n

Fig.8: Multirange voltmeter using potential divider<\/p>\r\n \r\n\r\nThe series resistances for the voltage ranges V1, V2,<\/em> V3 and V4<\/em> can be computed as follows:\r\n\r\n \r\n\r\nR1 = (m1 - 1)Rm<\/span>\r\n\r\n \r\n\r\nR2 = (m2 - m1)Rm<\/span>\r\n\r\n \r\n\r\nR3 = (m3 - m2)Rm<\/span>\r\n\r\n \r\n\r\nR4 = (m4 - m3)Rm<\/span>\r\n\r\n \r\n

This system has the advantage that all multipliers except the first have standard resistance values and can be obtained commercially in precision tolerances. The range multiplier, R1, is the only special resistor which must be manufactured to meet specific circuit requirements.<\/span><\/p>\r\n \r\n

Multi-range voltmeters are very effective for moderate range voltages. For higher-range voltages it is often desirable to use external resistors in connection with a given voltmeter.<\/span><\/p>\r\n \r\n

In using a multi-range voltmeter it is usual procedure first to connect the voltmeter to the highest voltage range terminal or set the switch to the highest voltage which the instrument will read. Then connect the instrument to the circuit and measure the voltage. Then decrease the ranges of the instrument until a good upscale reading is obtained on the voltmeter.<\/span><\/p>\r\n\r\n<\/div>\r\n

<\/div>\r\n \r\n\r\nQuestionnaire<\/strong>\r\n
    \r\n \t
  1. Explain the working of Ammeter shunts.<\/li>\r\n \t
  2. Describe the construction of shunts in detail.<\/li>\r\n \t
  3. What do you understand by voltage multipliers. Explain in detail.<\/li>\r\n \t
  4. Define and explain the different types of Multirange d.c. Voltmeters.<\/li>\r\n \t
  5. What do you understand by Multi-range Ammeters and Universal shunts.<\/li>\r\n<\/ol>\r\n\r\n\r\n\r\n
    you can view video on Analog Ammeters and Voltmeters II<\/strong><\/td>\r\n\"\"<\/a><\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n\u00a0 \u00a0 References:<\/strong>\r\n
      \r\n \t
    1. Electronic Measurements and Instrumentation by Bernard M. Oliver and John M. Cage.<\/li>\r\n \t
    2. Measurement and Instrumentation Principles by Alan S. Morris.<\/li>\r\n \t
    3. Instrumentation and Measurement in Electrical Engineering by Roman Malaric.<\/li>\r\n \t
    4. Measurement and Instrumentation Systems by William Bolton.<\/li>\r\n \t
    5. Engineering Measurements and Instrumentation by Leslie Frank Adams.<\/li>\r\n \t
    6. Electrical Measurements and Instrumentation by U. A. Bakshi.<\/li>\r\n \t
    7. Introduction to Measurements and Instrumentation by Arun K Ghosh.<\/li>\r\n<\/ol>","rendered":"
      \"epgp<\/a>
      \n<\/span><\/div>\n
      \n

      \u00a0 \u00a0 Ammeter Shunts:<\/strong><\/p>\n

       <\/p>\n

       <\/p>\n

      The basic movement of a d.c. ammeter is a PMMC d’Arsonva galvanometer. The coil winding of a basic movement is small and light and can carry very small currents since the construction of an accurate Instrument with a moving coil to carry currents greater than 100 mA is impracticable owing to the bulk anq weight of the coil that would be required. When heavy currents are to be measured, the major part of the current is bypassed through a low resistance called a “shunt”. Fig. 1 shows the basic movement (meter) and its shunt to produce an ammeter.<\/em> The resistance of the shunt can be calculated using conventional circuit analysis.<\/p>\n

       <\/p>\n

      \"\"<\/p>\n

       <\/p>\n

      where R<\/em>m<\/em>=<\/em> internal resistance of movement (i.e.<\/em> the coil), Im = Ifs = full scale deflection current of movement, Rsh=resistance of the shunt, Ish=shunt current, I=current to be measured.<\/p>\n

       <\/p>\n

      Since the shunt resistance is in parallel with the meter movement, the voltage drops across shunt and movement must be the same.<\/p>\n

       <\/p>\n

      or\u00a0\u00a0\u00a0 Ish Rsh =Im Rm<\/p>\n

       <\/p>\n

      Thus, Rsh =Im Rm\/ Ish<\/p>\n

       <\/p>\n

      But, Ish = I – Im<\/p>\n

       <\/p>\n

      Therefore, Rsh =Im Rm\/ (I- Im)<\/p>\n

       <\/p>\n

      Simplifying we get,\u00a0\u00a0\u00a0\u00a0 I\/Im = 1+ Rm\/Rsh<\/p>\n

       <\/p>\n

      This ratio of total current to the current in the movement is called Multiplying power of shunt.<\/p>\n

       <\/p>\n

      Multiplying power,\u00a0 m = I\/Im = 1+ Rm\/Rsh<\/p>\n

       <\/p>\n

      Resistance of shunt\u00a0\u00a0\u00a0 Rsh = Rm\/ (m-1)<\/p>\n

       <\/p>\n

      The shunt resistance used with a d’ Arsonval movement may consist of a coil of resistance wire within the case of the Instrument, or it may be external shunt having a very low resistance.<\/span><\/p>\n<\/div>\n

      \n

       <\/p>\n

      Construction of Shunts:<\/strong><\/p>\n

       <\/p>\n

      The general requirements for shunts are:<\/p>\n

       <\/p>\n

      (i)\u00a0 the temperature co-efficient of shunt and instrument should be low and should be as nearly as possible the same;<\/p>\n

       <\/p>\n

      (ii) the resistance of shunts should not vary with time;<\/p>\n

       <\/p>\n

      (iii)\u00a0 they should carry the current without excessive temperature rise;<\/p>\n

       <\/p>\n

      (iv)\u00a0 <\/em>they should have a low thermal electromotive force.<\/p>\n

       <\/p>\n

      ‘Manganin’ is usually used for shunts of d.c. instruments as it gives low value of thermal emf with copper although it is liable to corrosion and is difficult to solder. ‘Constantan’ is a useful material for a c. circuits since its comparatively high thermal emf, being unidirectional, is ineffective on these circuits.<\/p>\n

       <\/p>\n

      The construction of shunts is the same as that of low resistance standards. Shunts for low currents are enclosed in the meter casing but for currents above 200 A they are mounted separately.<\/p>\n

       <\/p>\n

      Shunts for heavy currents are mounted externally. Fig 2 shows an external shunt. It consists of evenly spaced sheets of resistive material welded into large blocks of heavy copper on each end of sheets. The resistance material has a very low temperature co-efficient and a low thermal electric effect between the resistance material and the copper. The heavy lugs (current terminals) on each end of the shunt carry the load current while the binding posts (potential terminals) on each end of the shunt are used to connect the ammeter to the shunt and carry only the current which passes through the meter (movement).<\/p>\n

       <\/p>\n

      \"\"<\/p>\n

       <\/p>\n

      Fig. 2 Shunt for heavy currents<\/p>\n

       <\/p>\n

      Meters using external shunts are usually designed to operate at a full scale voltage rating. These ratings are usually 50, 75 or 100 m V. This is the voltage across the potential terminals of the shunt when full scale current\u00a0flows through the load. Inasmuch as the current producing the meter deflection is a function of the voltage drop across the potential terminals of the shunt and the resistance of the instrument including the leads, the meter used with external shunts must have leads with a specified resistance to accompany the meter. Leads supplied with the instrument should never be changed and also no portion of the leads should be cut off otherwise it will lead to serious calibration errors.<\/span><\/p>\n

       <\/p>\n

      Arrangement for Temperature Effect Correction:<\/strong><\/p>\n

       <\/p>\n

      The temperature error can be eliminated when the shunt and the moving-coil are made of the same material and kept at the same temperature. This method, however, is not satisfactory in practice as the temperatures of the two parts are not likely to change at the same rate. An additional disadvantage of using copper shunts is that they are likely to be bulky as the resistivity of copper is small. Copper shunts are only occasionally used in instruments with built-in shunts.<\/span><\/p>\n<\/div>\n

      \n

      \"\"<\/p>\n

       <\/p>\n

      Fig. 3 : Meter shunt and swamp resistance<\/p>\n

       <\/p>\n

      The arrangement normally used is shown in the Fig.3. In this case, \u2018swamping\u2019 resistance of Manganin having a resistance 20 to 30 times the coil resistance is connected in series with the coil and a shunt of Manganin is connected cross this combination. Since copper forms a small fraction of the series combination, the proportion in which the currents would divide between the meter and the shunt would not change appreciably with the change in temperature.<\/p>\n

       <\/p>\n

      Multi-range Ammeters:<\/strong><\/p>\n

       <\/p>\n

      The current range of a d.c. ammeter may be further extended by a number of shunts, selected by a range switch. Such meter is called a multirange ammeter. Fig.4 shows a schematic diagram of multirange ammeter. The circuit has four shunts R<\/em>sh1<\/em> , R<\/em>sh2<\/em> , R<\/em>sh3<\/em> and R<\/em>sh4<\/em>,<\/em> which can be put in parallel with the meter movement to give four different current ranges I1, I2, I3 and I4.<\/p>\n<\/div>\n

      \"\"<\/p>\n

       <\/p>\n

      Fig. 4: Multi range ammeter<\/span><\/p>\n

      \n

       <\/p>\n

      Low range ammeters use a multiposition make before break switch (See in Fig. 4) provided on the case of the instrument. This type of switch is essential in order that the meter movement is not damaged when changing from the current range to another. If we provide an ordinary switch, the meter ramains without a shunt and as<\/em> such it is unprotected when the range is changed.<\/p>\n

       <\/p>\n

      When larger currents are used the connections are brought out to binding posts and the loads are connected directly to the binding post which is identified with the described current range. Multi-range ammeters are used for ranges from 1<\/em> to 50 A. When using a multi-range ammeter, first use the highest current range, then decrease the current range until good upscale reading is obtained.<\/p>\n

       <\/p>\n

      The universal shunt or Ayrton shunt is also used for multi-range ammeters. The advantage of an Ayrton shunt is that it eliminates the possibility of the meter being in the circuit without a shunt. But this advantage is gained at the cost of a higher meter resistance.<\/p>\n

       <\/p>\n

      Universal Shunt:<\/strong><\/p>\n

       <\/p>\n

      \"\"<\/p>\n

       <\/p>\n

      Fig. 5: Multi-range ammeter using universal shunt<\/p>\n

       <\/p>\n

      The universal shunt is presented here in a different form. Consider that the meter ranges have to be extended to I1, I2 and I3.<\/em> For the arrangement shown in Fig. 5, we have, for switch at position 1,<\/p>\n

       <\/p>\n

      Im Rm = (I1 – Im) R1<\/p>\n

       <\/p>\n

      Therefore, m1 = I1 \/ Im = 1+ Rm\/R1\u00a0 or<\/strong> R1 = Rm\/(m1-1)<\/p>\n

       <\/p>\n

      For switch at position 2, Im (R1 – R2 + Rm )= (I2 – Im) R2\u00a0<\/span>or R2 = (R1 + Rm)\/m2<\/span><\/p>\n

       <\/p>\n

      For switch at position 3, Im (R1 – R3 + Rm )= (I3 – Im) R3\u00a0<\/span>or R3 = (R1 + Rm)\/m3<\/span><\/p>\n

       <\/p>\n

      Thus the values of different selections of resistances <\/span>i.e.<\/em> (R1-R2), (R1- <\/span>R3),<\/em> and <\/span>R3<\/em> may be found.<\/span><\/p>\n<\/div>\n

      \n

       <\/p>\n

      Voltmeter Multipliers<\/strong><\/p>\n

       <\/p>\n

      A d’Arsonval basic meter movement is converted into a voltmeter by connecting a series resistance with it. This series resistance is known as a multiplier. The combination of the meter movement and the multiplier is put across the circuit whose voltage is to be measured.<\/p>\n

       <\/p>\n

      \"\"<\/p>\n

       <\/p>\n

      Fig. 6: Meter with a multiplier<\/p>\n

       <\/p>\n

      The multiplier limits the current through the meter so that it does not exceed the value for full scale deflection and thus prevents the movement form being damaged.<\/p>\n

       <\/p>\n

      The value of a multiplier, required to extend the voltage range, is calculated as under:<\/p>\n

       <\/p>\n

      Let<\/p>\n

       <\/p>\n

      l<\/em>m<\/em>=l<\/em>fs<\/em>=full <\/em>scale deflection current of meter,<\/p>\n

       <\/p>\n

      Rm = internal resistance of meter movement,<\/p>\n

       <\/p>\n

      R<\/em>s<\/em> = multiplier resistance,<\/p>\n

       <\/p>\n

      v <\/em>= voltage across the meter movement for current I<\/em>m<\/em>,<\/em><\/p>\n

       <\/p>\n

      V=fulI range voltage of instrument.<\/p>\n

       <\/p>\n

      For the circuit of Fig. 6, v=l<\/em>m<\/em> R<\/em>m<\/em><\/p>\n

       <\/p>\n

      V=l<\/em>m<\/em>(R<\/em>m<\/em>+ <\/em>Rs)<\/p>\n

       <\/p>\n

      Therefore, Rs = (V – l<\/em>m<\/em>R<\/em>m<\/em> )\/ l<\/em>m<\/em><\/p>\n

       <\/p>\n

      We can also express the result in terms of multiplying factor of multiplier.<\/span><\/p>\n

       <\/p>\n

      Multiplying factor for multiplier, m = V\/<\/span>v = 1 + Rs\/Rm<\/em><\/p>\n

       <\/p>\n

      Thus, resistance of multiplier Rs = (m-1)Rm<\/span><\/p>\n

       <\/p>\n

      Hence for the measurement of voltage <\/span>m<\/em> times the voltage range of the instrument the series multiplying resistance should be (m-1) times the meter resistance. Thus to extend the voltage range to 10 times the instrument range, Rs =9 <\/span>Rm.<\/em><\/p>\n<\/div>\n

      \n

       <\/p>\n

      Construction of Multipliers:<\/strong><\/p>\n

       <\/p>\n

      The essential requirements of multipliers are:<\/p>\n

       <\/p>\n

      (i)\u00a0 their resistance should not change with time;<\/p>\n

       <\/p>\n

      (ii) the change in their resistance with temperature should be small;<\/p>\n

       <\/p>\n

      (iii)\u00a0 they should be non-inductively wound for a.c. meters.<\/p>\n

       <\/p>\n

      The resistance materials used for multipliers are manganin and constantan.<\/p>\n

       <\/p>\n

      Multipliers are mounted inside the instrument case for voltages up to 500 V. For higher voltages, the multipliers may be mounted separately outside the case on a pair of binding posts to avoid excessive heating inside the case.<\/p>\n

       <\/p>\n

      Multirange d.c. Voltmeters<\/strong><\/p>\n

       <\/p>\n

      In a multirange voltmeter, different full scale voltage ranges may be obtained by the use of individual multiplier resistors or by a potential divider arrangement.<\/p>\n

       <\/p>\n

      1.\u00a0lndividual Multipliers<\/strong>: We can obtain different voltage ranges by connecting different values of multiplier resistors in series with the meter. The number of these resistors is equal to the number of ranges required. Fig. 7 shows multiplier resistors R<\/em>s1<\/em>,<\/em> Rs2, R<\/em>s3<\/em> and R<\/em>s4<\/em> which can be connected in series with the meter by a range selector switch. Consider that the ranges desired are V1, V<\/em>2<\/em>, V<\/em>3<\/em> and V<\/em>4<\/em>,<\/em> then the corresponding multiplier resistances can be obtained.<\/p>\n

       <\/p>\n

      \"\"<\/p>\n<\/div>\n

      \n

      Fig. 7 : Multirange Voltmeter<\/p>\n

       <\/p>\n

      Thus, we have<\/p>\n

       <\/p>\n

      Rs1 = (m1-1)Rm , Rs2 = (m2-1)Rm , Rs3 = (m3-1)Rm , Rs4 = (m4-1)Rm<\/p>\n

       <\/p>\n

      2. Potential Divider Arrangement:<\/strong><\/p>\n

       <\/p>\n

      Another multi-range voltmeter is shown in Fig. 8 in which the connections are made at the junctions of resistances R1. R2,<\/em> R3 and R4<\/em> in series to obtain the voltage range V1, V2,<\/em> V3 and V4.<\/em> These connections are brought out to binding posts on the instrument, and the instrument is connected to the proper binding post for the desired voltage range.<\/p>\n

       <\/p>\n

      \"\"<\/p>\n

       <\/p>\n

      Fig.8: Multirange voltmeter using potential divider<\/p>\n

       <\/p>\n

      The series resistances for the voltage ranges V1, V2,<\/em> V3 and V4<\/em> can be computed as follows:<\/p>\n

       <\/p>\n

      R1 = (m1 – 1)Rm<\/span><\/p>\n

       <\/p>\n

      R2 = (m2 – m1)Rm<\/span><\/p>\n

       <\/p>\n

      R3 = (m3 – m2)Rm<\/span><\/p>\n

       <\/p>\n

      R4 = (m4 – m3)Rm<\/span><\/p>\n

       <\/p>\n

      This system has the advantage that all multipliers except the first have standard resistance values and can be obtained commercially in precision tolerances. The range multiplier, R1, is the only special resistor which must be manufactured to meet specific circuit requirements.<\/span><\/p>\n

       <\/p>\n

      Multi-range voltmeters are very effective for moderate range voltages. For higher-range voltages it is often desirable to use external resistors in connection with a given voltmeter.<\/span><\/p>\n

       <\/p>\n

      In using a multi-range voltmeter it is usual procedure first to connect the voltmeter to the highest voltage range terminal or set the switch to the highest voltage which the instrument will read. Then connect the instrument to the circuit and measure the voltage. Then decrease the ranges of the instrument until a good upscale reading is obtained on the voltmeter.<\/span><\/p>\n<\/div>\n

      <\/div>\n

       <\/p>\n

      Questionnaire<\/strong><\/p>\n

        \n
      1. Explain the working of Ammeter shunts.<\/li>\n
      2. Describe the construction of shunts in detail.<\/li>\n
      3. What do you understand by voltage multipliers. Explain in detail.<\/li>\n
      4. Define and explain the different types of Multirange d.c. Voltmeters.<\/li>\n
      5. What do you understand by Multi-range Ammeters and Universal shunts.<\/li>\n<\/ol>\n\n\n\n
        you can view video on Analog Ammeters and Voltmeters II<\/strong><\/td>\n\"\"<\/a><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n

        \u00a0 \u00a0 References:<\/strong><\/p>\n

          \n
        1. Electronic Measurements and Instrumentation by Bernard M. Oliver and John M. Cage.<\/li>\n
        2. Measurement and Instrumentation Principles by Alan S. Morris.<\/li>\n
        3. Instrumentation and Measurement in Electrical Engineering by Roman Malaric.<\/li>\n
        4. Measurement and Instrumentation Systems by William Bolton.<\/li>\n
        5. Engineering Measurements and Instrumentation by Leslie Frank Adams.<\/li>\n
        6. Electrical Measurements and Instrumentation by U. A. Bakshi.<\/li>\n
        7. Introduction to Measurements and Instrumentation by Arun K Ghosh.<\/li>\n<\/ol>\n","protected":false},"author":3,"menu_order":20,"template":"","meta":{"pb_show_title":"on","pb_short_title":"","pb_subtitle":"","pb_authors":["prof-vinay-gupta"],"pb_section_license":""},"chapter-type":[],"contributor":[58],"license":[],"class_list":["post-357","chapter","type-chapter","status-publish","hentry","contributor-prof-vinay-gupta"],"part":3,"_links":{"self":[{"href":"https:\/\/ebooks.inflibnet.ac.in\/msp04\/wp-json\/pressbooks\/v2\/chapters\/357","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/ebooks.inflibnet.ac.in\/msp04\/wp-json\/pressbooks\/v2\/chapters"}],"about":[{"href":"https:\/\/ebooks.inflibnet.ac.in\/msp04\/wp-json\/wp\/v2\/types\/chapter"}],"author":[{"embeddable":true,"href":"https:\/\/ebooks.inflibnet.ac.in\/msp04\/wp-json\/wp\/v2\/users\/3"}],"version-history":[{"count":6,"href":"https:\/\/ebooks.inflibnet.ac.in\/msp04\/wp-json\/pressbooks\/v2\/chapters\/357\/revisions"}],"predecessor-version":[{"id":360,"href":"https:\/\/ebooks.inflibnet.ac.in\/msp04\/wp-json\/pressbooks\/v2\/chapters\/357\/revisions\/360"}],"part":[{"href":"https:\/\/ebooks.inflibnet.ac.in\/msp04\/wp-json\/pressbooks\/v2\/parts\/3"}],"metadata":[{"href":"https:\/\/ebooks.inflibnet.ac.in\/msp04\/wp-json\/pressbooks\/v2\/chapters\/357\/metadata\/"}],"wp:attachment":[{"href":"https:\/\/ebooks.inflibnet.ac.in\/msp04\/wp-json\/wp\/v2\/media?parent=357"}],"wp:term":[{"taxonomy":"chapter-type","embeddable":true,"href":"https:\/\/ebooks.inflibnet.ac.in\/msp04\/wp-json\/pressbooks\/v2\/chapter-type?post=357"},{"taxonomy":"contributor","embeddable":true,"href":"https:\/\/ebooks.inflibnet.ac.in\/msp04\/wp-json\/wp\/v2\/contributor?post=357"},{"taxonomy":"license","embeddable":true,"href":"https:\/\/ebooks.inflibnet.ac.in\/msp04\/wp-json\/wp\/v2\/license?post=357"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}