Measuring Instruments used for different electrical measurements

Measuring Instruments used for different electrical measurements

1. Galvanometer and its operation

2. Galvanometer A galvanometer is a device that is used to detect small electric current or measure its magnitude. The current and its intensity is usually indicated by a magnetic needle’s movement or that of a coil in a magnetic field that is an important part of a galvanometer. Some of the different types of galvanometer include Tangent galvanometer, Astatic galvanometer, Mirror galvanometer and Ballistic galvanometer. However, today the main type of galvanometer type that is used widely is the D’Arsonval / Weston type or the moving coil type. A galvanometer is basically a historical name that has been given to a moving coil electric current detector.

3. Working Principle of Galvanometer Moving-coil galvanometers are mainly divided into two types: Suspended coil galvanometer Pivoted-coil or Weston galvanometer A current-carrying coil when placed in an external magnetic field experiences magnetic torque. The angle through which the coil is deflected due to the effect of the magnetic torque is proportional to the magnitude of current in the coil.

4. Moving Coil Galvanometer Construction The moving coil galvanometer is made up of a rectangular coil that has many turns and it is usually made of thinly insulated or fine copper wire that is wounded on a metallic frame. The coil is free to rotate about a fixed axis. A phosphor-bronze strip that is connected to a movable torsion head is used to suspend the coil in a uniform radial magnetic field. Essential properties of the material used for suspension of the coil are conductivity and a low value of the torsional constant. A cylindrical soft iron core is symmetrically positioned inside the coil to improve the strength of the magnetic field and to make the field radial. The lower part of the coil is attached to a phosphor-bronze spring having a small number of turns. The other end of the spring is connected to binding screws.

5. Moving Coil Galvanometer Construction The spring is used to produce a counter torque which balances the magnetic torque and hence help in producing a steady angular deflection. A plane mirror which is attached to the suspension wire, along with a lamp and scale arrangement is used to measure the deflection of the coil. Zero-point of the scale is at the center.

6. Moving Coil Galvanometer Construction Figure 1.1 Construction of Galvanometer

7. Moving Coil Galvanometer Working Let a current I flow through the rectangular coil of n number of turns and a cross-sectional area A. When this coil is placed in a uniform radial magnetic field B, the coil experiences a torque τ. Let us first consider a single turn ABCD of the rectangular coil having a length l and breadth b. This is suspended in a magnetic field of strength B such that the plane of the coil is parallel to the magnetic field. Since the sides AB and DC are parallel to the direction of the magnetic field, they do not experience any effective force due to the magnetic field. The sides AD and BC being perpendicular to the direction of field experience an effective force F given by F = BIL

8. Moving Coil Galvanometer Working Figure 1.2 Force on coil

9. Moving Coil Galvanometer Working Using Fleming’s left-hand rule we can determine that the forces on AD and BC are in opposite direction to each other. When equal and opposite forces F called couple acts on the coil, it produces a torque. This torque causes the coil to deflect. We know that torque τ = force x perpendicular distance between the forces τ = F × b Substituting the value of F we already know, Torque τ acting on single-loop ABCD of the coil = BIL × b Where L x b is the area A of the coil, Hence the torque acting on n turns of the coil is given by τ = nIAB The magnetic torque thus produced causes the coil to rotate, and the phosphor bronze strip twists. In turn, the spring S attached to the coil produces a counter torque or restoring torque kθ which results in a steady angular deflection.

10. Moving Coil Galvanometer Working Under equilibrium condition: kθ = nIAB Here k is called the torsional constant of the spring (restoring couple per unit twist). The deflection or twist θ is measured as the value indicated on a scale by a pointer which is connected to the suspension wire. θ= ( nAB / k)I Therefore θ ∝ I The quantity nAB / k is a constant for a given galvanometer. Hence it is understood that the deflection that occurs the galvanometer is directly proportional to the current that flows through it.

11. Sensitivity of Moving Coil Galvanometer The general definition of the sensitivity experienced by a moving coil galvanometer is given as the ratio of change in deflection of the galvanometer to the change in current in the coil. S = dθ / dI The sensitivity of a galvanometer is higher if the instrument shows larger deflection for a small value of current. Sensitivity is of two types, namely current sensitivity and voltage sensitivity.

12. Sensitivity of Moving Coil Galvanometer Current Sensitivity: The deflection θ per unit current I is known as current sensitivity θ/I θ/I = nAB /k Voltage Sensitivity: The deflection θ per unit voltage is known as Voltage sensitivity θ/V. Dividing both sides by V in the equation θ = ( nAB / k)I; θ/V = ( nAB /V k)I = ( nAB / k)(I/V) = ( nAB /k)(1/R) R stands for the effective resistance in the circuit. It is worth noting that voltage sensitivity = Current sensitivity/ Resistance of the coil. Therefore under the condition that R remains constant; voltage sensitivity ∝ Current sensitivity.

13. Factors effecting Sensitivity of Galvanometer Number of turns in the coil Area of the coil Magnetic field strength B The magnitude of couple per unit twist k/ nA An increase in current sensitivity of a moving coil galvanometer may not necessarily result in an increase in voltage sensitivity. As the number of turns (length of the coil) are increased to increase the current sensitivity of the device, the resistance of the coil changes. This is because the resistance of the coil is dependent on factors like the length and area of the coil.

14. Applications of Galvanometer The moving coil galvanometer is a highly sensitive instrument due to which it can be used to detect the presence of current in any given circuit. If a galvanometer is a connected in a Wheatstone’s bridge circuit, pointer in the galvanometer shows null deflection, i.e.; no current flows through the device. The pointer deflects to the left or right depending on the direction of the current. The galvanometer can be used to measure; a) the value of current in the circuit by connecting it in parallel to low resistance. b) the voltage by connecting it in series with high resistance.

15. Conversion of Galvanometer to Ammeter A galvanometer is converted into an ammeter by connecting it in parallel with a low resistance called shunt resistance. Suitable shunt resistance is chosen depending on the range of the ammeter. Figure 1.3 Conversion of Galvanometer to Ammeter

16. Conversion of Galvanometer to Ammeter In the given circuit RG – Resistance of the galvanometer G- Galvanometer coil I – Total current passing through the circuit IG – Total current passing through the galvanometer which corresponds to full-scale reading Rs – Value of shunt resistance When current IG passes through the galvanometer, the current through the shunt resistance is given by IS = I – IG. The voltages across the galvanometer and shunt resistance are equal due to the parallel nature of their connection. Therefore RG .IG= (I- IG). Rs The value of Rs can be obtained using the above equation.

17. Conversion of Galvanometer to Voltmeter A galvanometer is converted into a voltmeter by connecting it in series with high resistance. A suitable high resistance is chosen depending on the range of the voltmeter. Figure 1.4 Conversion of Galvanometer to Voltmeter

18. Conversion of Galvanometer to Ammeter In the given circuit RG = Resistance of the galvanometer R = Value of high resistance G = Galvanometer coil I = Total current passing through the circuit IG = Total current passing through the galvanometer which corresponds to a full-scale deflection. V = Voltage drop across the series connection of galvanometer and high resistance. When current IG passes through the series combination of the galvanometer and the high resistance R;the voltage drop across the branch ab is given by V= RG.IG + R.IG The value of R can be obtained using the above equation.

19. Solved Problem 1 A moving coil galvanometer of resistance 100Ω is used as an ammeter using a resistance of 0.1Ω. The maximum deflection current in the galvanometer is 100μA. Find the current in the circuit, so that the ammeter shows maximum deflection. Solution: It is given that RG =100Ω , Rs = 0.1Ω, IG =100μA We know that RG .IG= (I- IG).RS Therefore I = (RG .IG+ IG.Rs)/ RS I= (1+RG/ RS). IG Substituting the given values, we get I= 100.1mA

20. Solved Problem 2 A galvanometer coil of 40Ω resistance shows full range deflection for a current of 4mA. How can this galvanometer be converted into a voltmeter of range 0-12V? Solution: As we know that V = IG (RG + R) R = V/ IG – RG = (12/ (4×10-3)) – 40 R = 2960 Ω

21. Advantages and Disadvantages of Galvanometer Advantages High sensitivity. Not easily affected by stray magnetic fields. The torque to weight ratio is high. High accuracy and reliability. Disadvantages It can be used only to measure direct currents. Develops errors due to factors like aging of the instrument, permanent magnets and damage of spring due to mechanical stress

22. Oscilloscope

23. Oscilloscope The cathode ray oscilloscope is probably the most versatile and useful instrument available for signal measurement. In its basic form, it is an analogue instrument and is often called an analogue oscilloscope. The analogue oscilloscope is widely used for voltage measurement, especially as an item of test equipment for circuit fault-finding, and it is able to measure a very wide range of both a.c . and d.c. voltage signals. Besides measuring voltage levels, it can also measure other quantities such as the frequency and phase of a signal.

24. Oscilloscope It can also indicate the nature and magnitude of noise that may be corrupting the measurement signal. The more expensive models can measure signals at frequencies up to 500 MHz and even the cheapest models can measure signals up to 20 MHz. One particularly strong merit of the oscilloscope is its high input impedance, typically 1 M, which means that the instrument has a negligible loading effect in most measurement situations. As a test instrument, it is often required to measure voltages whose frequency and magnitude are totally unknown.

25. Oscilloscope However, it is not a particularly accurate instrument and is best used where only an approximate measurement is required. In the best instruments, inaccuracy can be limited to 1% of the reading but inaccuracy can approach 10% in the cheapest instruments. Further disadvantages of oscilloscopes include their fragility (being built around a cathode ray tube) and their moderately high cost.  

26. Cathode Ray Tube The cathode ray tube, shown in the next slide, is the fundamental part of an oscilloscope. The cathode consists of a barium and strontium oxide coated, thin, heated filament from which a stream of electrons is emitted. The stream of electrons is focused onto a well defined spot on a fluorescent screen by an electrostatic focusing system that consists of a series of metal discs and cylinders charged at various potentials. Adjustment of this focusing mechanism is provided by controls on the front panel of an oscilloscope. An intensity control varies the cathode heater current and therefore the rate of emission of electrons, and thus adjusts the intensity of the display on the screen.

27. Cathode Ray Tube Figure 1.5 Cathode Ray Tube

28. Cathode Ray Tube The different types of controls are shown below: Figure 1.6 Controls of simple oscilloscope

29. Cathode Ray Tube Application of potentials to two sets of deflector plates mounted at right angles to one another within the tube provide for deflection of the stream of electrons, such that the spot where the electrons are focused on the screen is moved. The two sets of deflector plates are normally known as the horizontal and vertical deflection plates, according to the respective motion caused to the spot on the screen.

30. Cathode Ray Tube In the oscilloscope’s most common mode of usage measuring time-varying signals, the unknown signal is applied, via an amplifier, to the y-axis (vertical) deflector plates and a time-base to the x-axis (horizontal) deflector plates. In this mode of operation, the display on the oscilloscope screen is in the form of a graph with the magnitude of the unknown signal on the vertical axis and time on the horizontal axis.

31. Cathode Ray Tube Channel: One channel describes the basic subsystem of an electron source, focusing system and deflector plates. This subsystem is often duplicated one or more times within the cathode ray tube to provide a capability of displaying two or more signals at the same time on the screen. The common oscilloscope configuration with two channels can therefore display two separate signals simultaneously.

32. Cathode Ray Tube Single Ended Input: This type of input only has one input terminal plus a ground terminal per oscilloscope channel and, consequently, only allows signal voltages to be measured relative to ground. It is normally only used in simple oscilloscopes. Differential Input: This type of input is provided on more expensive oscilloscopes. Two input terminals plus a ground terminal are provided for each channel, which allows the potentials at two non-grounded points in a circuit to be compared. This type of input can also be used in single-ended mode to measure a signal relative to ground by using just one of the input terminals plus ground.

33. Cathode Ray Tube Time Base Control: The purpose of a time-base is to apply a voltage to the horizontal deflector plates such that the horizontal position of the spot is proportional to time. This voltage, in the form of a ramp known as a sweep waveform, must be applied repetitively, such that the motion of the spot across the screen appears as a straight line when a d.c. level is applied to the input channel.

34. Cathode Ray Tube Time Base Control: Furthermore, this time-base voltage must be synchronized with the input signal in the general case of a time-varying signal, such that a steady picture is obtained on the oscilloscope screen. The length of time taken for the spot to traverse the screen is controlled by a time/div switch, which sets the length of time taken by the spot to travel between two marked divisions on the screen, thereby allowing signals at a wide range of frequencies to be measured

35. Cathode Ray Tube Vertical Sensitivity Control: This consists of a series of attenuators and pre-amplifiers at the input to the oscilloscope. These condition the measured signal to the optimum magnitude for input to the main amplifier and vertical deflection plates, thus enabling the instrument to measure a very wide range of different signal magnitudes. Selection of the appropriate input amplifier/attenuator is made by setting a volts/div control associated with each oscilloscope channel. This defines the magnitude of the input signal that will cause a deflection of one division on the screen.

36. Cathode Ray Tube Display Position Control: This allows the position at which a signal is displayed on the screen to be controlled in two ways. The horizontal position is adjusted by a horizontal position knob on the oscilloscope front panel and similarly a vertical position knob controls the vertical position. These controls adjust the position of the display by biasing the measured signal with d.c. voltage levels.

37. Digital Storage Oscilloscope Digital storage oscilloscopes consist of a conventional analogue cathode ray oscilloscope with the added facility that the measured analogue signal can be converted to digital format and stored in computer memory within the instrument. This stored data can then be reconverted to analogue form at the frequency necessary to refresh the analogue display on the screen. This produces a non-fading display of the signal on the screen.

38. Digital Storage Oscilloscope The signal displayed by a digital oscilloscope consists of a sequence of individual dots rather than a continuous line as displayed by an analogue oscilloscope. However, as the density of dots increases, the display becomes closer and closer to a continuous line, and the best instruments have displays that look very much like continuous traces. The density of the dots is entirely dependent upon the sampling rate at which the analogue signal is digitized and the rate at which the memory contents are read to reconstruct the original signal. Inevitably, the speed of sampling etc. is a function of cost, and the most expensive instruments give the best performance in terms of dot density and the accuracy with which the analogue signal is recorded and represented.

39. Digital Storage Oscilloscope Besides their ability to display the magnitude of voltage signals and other parameters such as signal phase and frequency, some digital oscilloscopes can also compute signal parameters such as peak values, mean values and r.m.s . values . In addition, digital oscilloscopes often have facilities to output analogue signals to devices like chart recorders and output digital signals

40. Resistance Measurement Devices that convert the measured quantity into a change in resistance include the resistance thermometer, the thermistor, the wire-coil pressure gauge and the strain gauge. The standard devices and methods available for measuring change in resistance, which is measured in units of ohms , include the d.c. bridge circuit, the voltmeter–ammeter method, the resistance-substitution method, the digital voltmeter and the ohmmeter. Apart from the ohmmeter, these instruments are normally only used to measure medium values of resistance in the range of 1 to 1 M . Special instruments are available for obtaining high-accuracy resistance measurements outside this range.  

41. Resistance Measurement D.C. Bridge Circuit: D.C. bridge circuits, as discussed earlier, provide the most commonly used method of measuring medium value resistance values. The best measurement accuracy is provided by the null-output-type Wheatstone bridge, and inaccuracy figures of less than 0.02% are achievable with commercially available instruments. Deflection-type bridge circuits are simpler to use in practice than the null-output type, but their measurement accuracy is inferior and the non-linear output relationship is an additional difficulty. Bridge circuits are particularly useful in converting resistance changes into voltage signals that can be input directly into automatic control systems.  

42. Resistance Measurement Voltmeter-ammeter method: The voltmeter–ammeter method consists of applying a measured d.c. voltage across the unknown resistance and measuring the current flowing. Two alternatives exist for connecting the two meters, as shown in figure on next slide. In part (a), the ammeter measures the current flowing in both the voltmeter and the resistance. The error due to this is minimized when the measured resistance is small relative to the voltmeter resistance. In the alternative form of connection, in part (b), the voltmeter measures the voltage drop across the unknown resistance and the ammeter.

43. Resistance Measurement Voltmeter-ammeter method:

44. Resistance Measurement Voltmeter-ammeter method: Here, the measurement error is minimized when the unknown resistance is large with respect to the ammeter resistance. Thus, method (a) is best for measurement of small resistances and method (b) for large ones. Having thus measured the voltage and current, the value of the resistance is then calculated very simply by Ohm’s law. This is a suitable method wherever the measurement inaccuracy of up to 1% that it gives is acceptable.  

45. Resistance Measurement Resistance-substitution method: In the voltmeter–ammeter method above, either the voltmeter is measuring the voltage across the ammeter as well as across the resistance, or the ammeter is measuring the current flow through the voltmeter as well as through the resistance. The measurement error caused by this is avoided in the resistance-substitution technique. In this method, the unknown resistance in a circuit is temporarily replaced by a variable resistance. The variable resistance is adjusted until the measured circuit voltage and current are the same as existed with the unknown resistance in place. The variable resistance at this point is equal in value to the unknown resistance.

46. Resistance Measurement Ohmmeter: The ohmmeter is a simple instrument in which a battery applies a known voltage across a combination of the unknown resistance and a known resistance in series, as shown in figure below.

47. Resistance Measurement Ohmmeter: Measurement of the voltage, Vm , across the known resistance, R, allows the unknown resistance, Ru, to be calculated from: where Vb is the battery voltage. Ohmmeters are used to measure resistances over a wide range from a few milliohms up to 50 M The measurement inaccuracy is 2% or greater, and ohmmeters are therefore more suitable for use as test equipment rather than in applications where high accuracy is required. Most of the available versions contain a switchable set of standard resistances, so that measurements of reasonable accuracy over a number of ranges can be made.