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Transcript
CHAPTER 2 Voltage and Current Measurement 1 Introduction of Electric Circuit The ultimate goal of the circuit theory is to predict currents and voltages in complex circuits (circuit analysis) and to design electrical circuits with desired properties. The circuits are built with circuit elements. Some of these elements are voltmeters, ammeters, wires, resistors, capacitors, inductors, and switches. 2 Ammeters Electrical currents can be measured with an ammeter. To measure the current in the wire shown in Fig. 1a, the wire should be cut and the ammeter should be inserted. The current will flow through the ammeter (Fig. 1b). 3 Cont’…Ammeters An ideal ammeter should have a negligible effect on the circuit. This means that the voltage difference between its two terminals (A and B) should be zero. In other words, the internal resistance (impedance) of an ideal ammeter is zero. 4 Voltmeter To measure voltage, the two terminals of a voltmeter should be connected to two points in the circuit between which the potential difference is measured. An ideal voltmeter should not affect the circuit. Therefore, current through the voltmeter (this is current in Fig.2) should be zero. In other words, internal resistance (impedance) of an ideal voltmeter is infinity. A real voltmeter is never ideal and its impedance is finite. 5 Kirchhoff Laws Kirchhoff laws are applicable to both the linear and not linear circuits. They provide a universal tool for circuit analysis. Kirchhoff ’s Current Law (KCL) The sum of the currents entering a node is equal to the sum of currents leaving the node. A node is a point where two or more wires are interconnected. Kirchhoff ’s Voltage Law (KVL) An algebraic sum of voltages across all elements along any closed path is zero. Algebraic sum means that we should take “+” sign if the voltage rises after a circuit element and “–“ sign if the voltage drops after a circuit element. 6 Cont’…Kirchhoff Laws Analysis of a circuit. General rules: 1. Identify every loop which does not contain another loop (such a loop is called mesh). Assign a current for every loop. The current direction can be chosen arbitrary. This step ensures that the Kirchhoff’s current law is automatically satisfied. 7 2. Use Ohm’s law (or other relations between voltages and currents if the circuit includes capacitors, inductors, diodes, etc) to calculate the voltage across all elements along every mesh and write equations (for every mesh) using Kirchhoff’s voltage law. Important! If two currents flow through an element, the currents should be added like vectors (their directions are important!). 3. Solve the equations. Example 1 Consider the circuit below. KVL @ mesh 1; I1R1 ( I1 I 2 ) R3 V0 0 (1) KVL @ mesh 2; I 2 R2 I 2 R4 ( I 2 I1 ) R3 0 (2) 8 Example 2 Kirchhoff Law when applied to capacitor and inductor usually produce differential equations. KVL dI L IR VC Vs (t ) 0 dt 9 Electrical Indicating Instruments and Measurement Electrical instruments are classified into two (2) 1. Absolute instruments The value of the electrical quantity to be measured are given by these instruments. The quantity are measured in terms of constants and from deflection of the instruments only. Example : Tangent galvanometer. 10 2. Secondary instruments The value of the electrical quantity to be measured is determined from the deflection of these instruments. With an absolute instrument these instruments are calibrated. There are three categories of secondary instruments 1. Indicating instruments 2. Recording instruments 3. Integrating instruments 11 Categories of Secondary Instruments 1. Indicating instruments The value of the electrical quantity is indicated by these instruments at the time when it is being measured. Pointers moving over the scale give the indication. • Examples: Ammeters, volmeters and wattmeter 2. Recording instruments A continuous record of variations of the electrical quantity over a long period of time is given by these instruments. It has a moving system which carries an inked pen which rest tightly on a graph chart. Examples: Graphic recorders and Galvanometer recorders 12 Cont’… 3. Integrating instruments The total amount of either electricity or electrical energy supplied over a period of time is measured by these instruments. Example : Ampere hour meters, watt hour meter, energy meters 13 1.0 Current Measurement 14 Current Basic analog measurement of current –uses inductive force on the current carrying conductor in magnetic field. This force can be used to measure the needle deflection on a display. Direct Current (DC) Charges flow in one direction commonly found in many low-voltage applications, especially where these are powered by batteries Alternating Current (AC) Flow of electric charge changes direction regularly Example: audio & radio signal Home & school use AC 15 Permanent Magnet Moving Coil Instrument (PMMC) There are TWO(2) types of moving coil instruments; Permanent Magnet Moving Coil Dynamometer Type 16 Construction It consists of a permanent magnet with soft iron pieces. The U-shape magnet is widely used. A coil of many turn is wound on aluminium frame. The coil is can move freely move in the field of a permanent magnet. The soft iron coil is mounted between the poles of permanent magnet giving a very narrow gap. The pointer is carried by the spindle and moving over a graduated scale. 17 Cont’d… The control torque is provide by two phosphor bronze hair springs. Eddy current damping is produced by movement of the aluminium former moving in the magnetic fields of permanent magnets. Phospher – bronze springs, pointer, jewel bearings etc. The current is passed into and out of the coil by means of phospher bronze hair springs provided at both ends. The springs also provide the controlling torque. The aluminium frame supports the coil. It also provides a damping torque by the eddy currents induced in it. 18 Operation When the current to be measured is passed to the moving coil, a deflecting torque, Td is produced on account of reaction of the permanent magnetic field with the coil magnetic field. The direction of deflecting torque can be determined by applying Fleming’ Left Hand Rule. The moving system turns through an angle q at which position the tightened control spring produces a back torque Tc equal to Td. The pointer stabilizes at this stage and gives the reading. 19 Advantages It consumes very small power They have no hysteresis losses They have high torque-weight ratio Their scale is uniform They have very effective and efficient eddy current damping 20 Disadvantages Some errors are set in due to ageing of control springs and the permanent magnet. High cost These instruments cannot be used for AC measurement Friction and temperature causes for error 21 Reason for use on DC only The depletion of a moving coil meter depend on polarity of meter connection. For one polarity of connection, the deflecting torque is acting forward. When connection is reversed, the deflection is also reversed. So it is cannot be used for AC measurement but can be used for DC measurement. 22 Dynamometer Type There are two fixed coils F1 and F2 held parallel to each other. They are electrically connected in series. When a current is passed through them, a uniform magnetic field is produced between the two fixed coils. 23 Cont’d… Within this magnetic field a moving coil is placed and support by a spindle and jewel bearings. The spindle carries two control springs that also serve as current leads to the moving coil. Moving coil can be connected either in series or parallel with fixed coil. Series connection – voltmeter Parallel connection – ammeter 24 Advantages It is free from hysteresis and eddy current losses because there is no iron core. It can be used for AC as well as DC measurement. It has a fairly high degree of accuracy. 25 Disadvantages The power loss is high Torque/weight ratio is small Scale is non-uniform Subjected to errors by stray magnetic fields. Error due to mutual induction of coils while measuring AC. It is comparatively more expensive. Friction and temperature causes for error 26 Ammeter An ammeter is an instrument for measuring the electric current in amperes in a branch of an electric circuit. It must be placed in series with the measured branch, and must have very low resistance to avoid significant alteration of the current it is to measure. connecting an ammeter in parallel can damage the meter 27 Ammeter – Principle of Operation The earliest design is the D'Arsonval galvanometer or moving coil ammeter (respond to ac only) It uses magnetic deflection, where current passing through a coil causes the coil to move in a magnetic field The voltage drop across the coil is kept to a minimum to minimize resistance across the ammeter in any circuit into which the it is inserted. Moving iron ammeters use a piece or pieces of iron which 28 move when acted upon by the electromagnetic force of a fixed coil of (usually heavy gauge) wire (which respond to both dc & ac) Ammeter Design 29 An ammeter is placed in series with a circuit element to measure the electric current flow through it. The meter must be designed offer very little resistance to the current so that it does not appreciably change the circuit it is measuring. To accomplish this, a small resistor is placed in parallel with the galvanometer to shunt most of the current around the galvanometer. Its value is chosen so that when the design current flows through the meter it will deflect to its full-scale reading. A galvanometer full-scale current is very small: on the order of milliamperes. 30 Basic DC Ammeter Circuit In most circuits, Ish >> Im Ammeter Where 31 Rsh = resistance of the shunt Rm = internal resistance of the meter movement (resistance of the moving coil) Ish = current through the shunt Im = full-scale deflection current of the meter movement I = full-scale deflection current for the ammeter D’Ársonval meter movement used in ammeter circuit The voltage drop across the meter movement is Vm I m Rm The shunt resistor is parallel with the meter movement, thus the voltage drop for both is equal Then the current through the shunt is, Vsh Vm I sh I I m By using Ohm’s law, Then we can get shunt resistor as Vsh I m Rm I m Im Rsh Rm Rm I I m I sh I sh I sh 32 Example 1.1 Calculate the value of the shunt resistance required to convert a 1-mA meter movement, with a 100-ohm internal resistance, into a 0- to 10-mA ammeter. 33 The Aryton Shunt The purpose of designing the shunt circuit is to allow to measure current I that is some number n times larger than Im. The number n is called a multiplying factor and relates total current and meter current as I nI m (1) We can get shunt resistance with n times larger than Im is Rm Rsh (2) n 1 34 Examples 1.2 A 100 µA meter movement with an internal resistance of 800 Ω is used in a 0 - to 100 mA ammeter. Find the value of the required shunt resistance. 35 Advantages of the Aryton Eliminates the possibility of the meter movement being in the circuit without any shunt resistance. May be used with a wide range of meter movements. Aryton shunt circuit 36 Cont’d... The individual resistance values of the shunts are calculated by starting with the most sensitive range and working toward the least sensitive range The shunt resistance is Rsh Ra Rb Rc On this range the shunt resistance is equal to Rsh and can be computed by Equation 37 Rm Rsh n 1 Cont’... I m ( Rsh Rm ) Rb Rc I2 I m ( Rsh Rm ) Rc I3 Rb ( Rb Rc ) Rc Ra Rsh ( Rb Rc ) 38 Ammeter Insertion Effects Inserting an ammeter in a circuit always increases the resistance of the circuit and reduces the current in the circuit. This error caused by the meter depends on the relationship between the value of resistance in the original circuit and the value of resistance in the ammeter. ** For high range ammeter, the internal resistance in the ammeter is low. ** For low range ammeter, the internal resistance in the ammeter is high. 39 E Ie R1 E Im R1 Rm Fig 2-4: Series circuit with ammeter 40 Cont’d... hence; Im R1 I e R1 Rm Therefore Insertion error = 41 Im 1 100% Ie Example 1.3 A current meter (ammeter) that has an internal resistance of 78 ohms is used to measure the current through resistor Rc in Figure below. Determine the percentage of error of the reading due to ammeter insertion. 42 AMMETER SHUNT An ammeter may be use to measure greater current than that which the instrument itself can carry with the help of shunts. An ammeter shunt is merely low resistance that is placed in parallel with the coil circuit of the instrument in order to measure fairly large current. The circuit diagram for a shunt and milli-ampere meter for measuring large current is shown. 43 Galvanometer It is an electromechanical transducer that produces a rotary deflection, through a limited arc, in response to electric current flowing through its coil. Galvanometer has been applied to devices used in measuring, recording, and positioning equipment. 44 Galvanometer – Principle of Operation Such devices are constructed with a small pivoting coil of wire in the field of a permanent magnet. The coil is attached to a thin pointer that traverses a calibrated scale. A tiny spring pulls the coil and pointer to the zero position. In some meters, the magnetic field acts on a small piece of iron to perform the same effect as a spring. When a direct current (DC) flows through the coil, the coil generates a magnetic field. This field acts with or against the permanent magnet. The coil pivots, pushing against the spring, and moving the pointer. The hand points at a scale indicating the electric current. A useful meter generally contains some provision for damping the mechanical resonance of the moving coil and pointer so that the pointer position smoothly tracks the current without excess vibration. 45 Galvanometer – Application Are used to position the pens of analog chart (example: electrocardiogram) 46