Measurement of Electrical Current, Voltage and Resistance / 1 4. MEASUREMENT OF ELECTRICAL CURRENT, VOLTAGE AND RESISTANCE 4.1. PRINCIPLES OF MEASUREMENTS Electrical voltage and current are two important quantities in an electrical network. The voltage is the effort variable without which no current is available. It is measured across an electrical circuit element or branch of a circuit. The device that measures the voltage is the voltmeter. The current is the flow variable that represents net motion of the charged particles (electrons in solids, ions in a liquid) in a given direction. The product of the two yields the instantaneous electrical power. The ratio of the voltage to the current is the impedance. The current is measured by an ammeter (also called an ampermeter). Ammeters are connected in series with the load to measure the current in the load. Eventually, the ammeters require breaking the current loop to place it into the RT A circuit. The voltmeter connection is rather easy since it + IL V is connected without disturbing the circuit layout. VT RL - VL Therefore, most electrical measurements require determination of the voltage rather than the current due Figure 4.1. Connections for an the ease of measurement. Connections of ammeters and ammeter and a voltmeter. voltmeters are illustrated in Figure 4.1. The current generates a magnetic field around the current carrying conductor. It is also possible to check out the size of the current by sensing the magnetic field strength. This is carried out by clamp-on type ammeters. The electrical resistance of a circuit component is measured using an ohmmeter that applies a voltage across and determines the current passing through the component. Voltmeters and ammeters display the results as deflections of dials on calibrated screens or numerical values on alphanumeric displays as illustrated in Figure 4.2. Both types are connected to the circuit via sensing Figure 4.2. Analog and digital voltmeters leads and indicate the voltage. However, their Measurement of Electrical Current, Voltage and Resistance / 2 internal operations and user interfaces are different. The first type forms the analog meters that will be discussed in this chapter. The second category will be discussed in the next chapter under the title of digital voltmeters. 4.2. MC BASED MEASURING INSTRUMENTS 4.2.1. MC in Analog Electrical Measuring Instruments The standard MC instrument indicates positive DC currents (IMC) as deflection on the scale. The galvanometer displays both positive and negative currents. The moving IFSD RMC coil is usually made up of a very thin wire. The maximum current that + - gives full‐scale deflection IFSD is in the order of 0.1 to 10 mA and coil VMC resistance RMC 10 to 1000 Ω. The maximum deflection angle is about Figure 4.3. Model of MC 100°. The current through the moving coil IMC is limited by the IFSD. A voltage drop VMC = IMCRMC occurs across the coil. The moving coil can represented by the full‐scale deflection current IFSD and coil resistance RMC as shown in Figure 4.3. 4.2.2. Ammeters Basic DC Ammeter (Ampermeter) The current capacity of the meter can be expended by adding a resistor in RMC parallel with the meter coil as shown in Figure 4.4. The input current is I FSD + - shared between the coil resistance RMC and the parallel resistance that is VMC called the shunt RSH. As the maximum input current IT flows in, the coil takes RSH IFSD and remaining (IT ‐ IFSD) is taken by the shunt resistor. Voltage developed IT (IT - IFSD) across the meter is RM MC = RIV MCFSD = ( T − )RII SHFSD ..........................................(4.1) Figure 4.4. DC Ammeter. The meter resistance RM seen between the input terminals is VMC RM == MC // RR SH ................................................................................................. (4.2) IT Example 1 Calculate the multiplying power of a shunt of 200 Ω resistance used with a galvanometer of 1000 Ω resistance. Determine the value of shunt resistance to give a multiplying factor of 50. 9 Ifsdx1000 = (IT – Ifsd)x200 yielding IT = 6xIfsd. 9 For IT=50xIfsd, 1000xIfsd=(50-1)xIfsdxRsh yielding Rsh =1000/49 = 20.41 Ω Measurement of Electrical Current, Voltage and Resistance / 3 Multi­Range Ammeter Switch The parallel resistance (shunt) can be changed to suit poles different full‐scale current requirements as indicated in the previous example. The function can be accommodated by Rotary switch using a set of resistors and selecting them one by one. The arm switch however must be of make‐before‐break type Figure 4.5. Make‐before‐break type (Figure 4.5) that makes the contact with the new position switch. before it breaks the old connection. This eliminates the chance of forcing the full input current through the moving coil during changing the position of the switch. Example 2 Design a multi‐range DC ammeter using the basic movement with an internal resistance RMC= 50 Ω and full‐scale deflection current IMC= IFSD= 1 mA. The ranges required 0‐10 mA, 0‐50 mA, 0‐100 mA and 0‐500 mA as illustrated in Figure 4.6. 9 VMC = IMCxRMC = 50 mV 9 For range-1 (0-10 mA) RSH1= 50/9 =5.56 Ω IT IFSD RMC 0 500 mA RSH1 0 → 500 mA 0 100 mA 0 50 mA Rotary RSH2 0 10 mA 0 → 100 mA selector R switch SH3 0 → 50 mA R SH4 0 → 10 mA Multi-range ammeter scale Multi-range ammeter circuit Figure 4.6. A multi-range ammeter circuit and scale for example 2. 9 For range-2 (0-50 mA) RSH2= 50/49 =1.02 Ω 9 For range-3 (0-100 mA) RSH3= 50/99 =0.505 Ω 9 For range-4 (0-500 mA) RSH4= 50/499 =0.1 Ω Example 3 Design a multi‐range DC ammeter using the basic movement with an internal resistance RMC= 50 Ω and full‐scale deflection current IMC= IFSD= 10 mA. The ranges required 0‐0.1 A, 0‐1 A, 0‐10 A and 0‐ 100 A. Measurement of Electrical Current, Voltage and Resistance / 4 9 VMC = IMCxRMC = 500 mV 9 For range-1 (0-0.1 A) RSH1= 500/90 = 5.56 Ω 9 For range-2 (0-1 A) RSH2= 0.5/0.99 = 0.505 Ω 9 For range-3 (0-10 A) RSH3= 0.5/9.99 = 0.05 Ω 9 For range-4 (0-100 A) RSH4= 0.5/99.99 = 0.005 Ω 4.2.3. Voltmeters IFSD RS RMC Basic DC Voltmeter The moving coil can be used as a voltmeter by adding a series + - + - VS VMC resistance RS as illustrated in Figure 4.7. The input voltage is VM divided between the coil resistance RMC and RS. Current passing + - RM through both resistors is IMC which is limited by the full‐scale deflection current IFSD of the coil. The full‐scale input voltage Figure 4.7. Basic DC voltmeter. VM = IFSD(RS+RMC) ................................................. (4.3) The input impedance seen is RM = RS + RMC ..................................................................................................................... (4.4) However, with RS>>RMC, RM is approximately equal to RS and VM ≅ IFSDRS. Example 4 The coil of a moving coil voltmeter is 4 cm long and 3 cm wide and has 100 turns on it. The control spring exerts a torque of 2.4x10-4 N-m when the deflection is 100 divisions on the full scale. If the flux density of the magnetic filed in the air-gap is 0.1 Wb/m2, estimate the resistance that must be put in series with the coil to give one volt per division. The resistance of the voltmeter coil may be neglected. -4 -4 9 TEM = TSP ⇒ 2.4x10 = 100x0.1x12x10 xIFSD ⇒ IFSD =20 mA. Therefore, current per division is 0.2 mA. Assuming that RMC is negligibly small compared to RS : RS = 5 kΩ Example 5 A moving coil instrument gives full-scale deflection of 10 mA when the potential difference across its terminals is 100 mV. Calculate: a. The shunt resistance for a full scale corresponding to 100 mA; 9 RSH = 100 / 90 = 1.11 Ω b. The resistance for full scale reading with 1000 V; 9 RMC = 100 /10 = 10 Ω; RS + RMC = (1000 / 10) kΩ = 100 kΩ yielding RS = 100 kΩ (RMC is negligible) Measurement of Electrical Current, Voltage and Resistance / 5 c. The power dissipated by the coil and by the external resistance in each case. 2 9 Power dissipated by the coil, PC = IM xRMC = 1 mW; 2 9 PSH = VM /RSH = 9 mW 2 9 PS = VM /RS = 10 W. Multi­Range Voltmeter The series resistance can be changed to suit different full‐scale voltage requirements as shown in Figure 4.8. Resistors are organized either in parallel fashion (conventional connection) as in the case Voltage to be measured RS2 RS1 RMC RS4 IFSD 0 → 1000 V RMC 1 RS3 0 → 100 V RS3 2 V R M S2 0 → 50 V 3 Rotary 4 selector RS1 0 → 10 V RS4 0 → 1000 V switch Multi-range voltmeter circuit Multi-range voltmeter circuit Parallel connection Series connection Figure 4.8. Parallel and series resistance connections for a multi-range voltmeter. of ammeter and selecting them one by one or all connected in series like a voltage divider (modified connection). The switch however must be of break‐before‐ Switch make type (Figure 4.9) that breaks the contact with the old poles position before it makes it with the new position. This Rotary eliminates the chance of forcing a current larger than the switch arm full‐scale current through the moving coil during changing Figure 4.9.