Question

Course : Electrical engineering Topic: Electrical Measurements 5.(a). Describe how pendulum scale is used for measurement of force (b). A barium titanate pickup has the dimensions of 5 mm x 5 mm x 1.25 mm. The acting force is 5N. The charge sensitivity of the material is 150 pc/N and permittivity is 12.5x 10-9 F/m. IF The modulus of elasticity of materials is 12.5 x 106 N/m². Calculate the strain, charge and capacitance. (c). (a) When a high value of gauge factor is desirable, What type of strain the should be used and why? (b) Explain its working. (c) What are its specific advantages?

Answer 1

o M TTTTTTTTTTTTTTTTT HHH Principle It is a deflection tyhe instrument. It converts applied unknown force into torque which is then balanced by the torque of a standard maus. In this case the standard mau is fixed and arranged was a pendulum. Construction It is contains a frame that carouy supporting, Kiblone' which awu. Connected to sectors. The loading tapes cou.connected to sectous and load mods. The lead rods are altached to weighing, flat- film to which an unknown face is applied. An equalizer Jam is corrected Metusten the two schous to which coumt weights care attached. A rack and pinion carries a chointer that moves on a scale which is calibrated in terms or were Working: . When the face to be measured is applied to the load rod, the loding, blons are fulled downward du. Jo which thu sestou sital, which in Susun causes the counter weights to move outwards. This increase the counter weight effective movement until the torque produced by the unknown force and movement produced by the counter weight balance each other. When these two are equilibrium condition is obtained. While the equilibrium state is establishing the equalizer beam moves doon. Due to this rack also moves down and hence the pinion rotates.

> when the pinion rotates the pointer connected to it moves and indicates a new hosition on the calibrated scale. In this way the applied force or weight is measured directly.

Ans b. Given that, length of the crystal, L= 45 mm Breadth of the crystal, b=5 mm Thicknes of the crystal, t = 1.25mm forcibe acting on crystal, F-5N charge sensitiwilip cof crystal, d = 150p Clw Permitivity, es 15X10-9F/m Young's modulus, E = 12x10 N/my Jo determine, i) Strain lli) charge (iii) capacitance Area of hlatis, A - 5x5x106 - 25x10m presure, P- F/A- 35x10-6 2x105 - 0.axio“Nim" Voltage senstiilip.go.co = 150X10-12 12.5X10-9-0012 - 12x10-3 Vom IN voltage generated, Eo - gt P - laxio-3x1.25x10-3x0.2x106 - 3V 6 strus strus sbrain - Young's modules cof elasticity D-ax106 [i Sibrws: Preescore] 12X106 -0.016 ja

(ii) charge, a charge, Q = df : = 150X10-12X5 - 750 PC (iii) capacitance, capacitance, C = % - - 750 x10-12 3 . = 250 pF

Ang a semiconductor that, the a strain ga c Ans:caWhen a high value of gauge factor is required, a . Semiconductor Strain gauge is preferred We know that, the general equation for the gauge factor (or the sensitivity of a strain gauge is given as, ...... From the given relation, ... G-DR/R 4 dL/L Conclusion can be drawn that a relatively high change in resistance will result in a high Value of gauge Factor. in metallic resistance Strain gauges, the change in resistance Occurs mainly due to the change in dimensions and the change in resistivity is almost negligible. " Hence equation (0) reduces to, G = 1+2v Usually, Posssion's ratio v=0.3 (for most of the metals working in elastic limit) :..G=2 The gauge factor can be imporoved, if the change in resistivity is brought into effect.

Unlike metallic gauges, in Semiconductor strain gauges, when Strain is applied the change in resistance occurs mainly due to piezo - resistive effect. The change in resistivity due to strain is known as piezo - resistive effect. Hence, for Semiconductor strain gauges, the term dplp comes into effect in gauge factor Gauge factor de la comes into effect in equation le, G = 1 +2y+dplp dL/L = 1+ 2y + TE Where , T = Piezo - resistive coefficient E = Young's modulus of elasticity of the material. As the resistance of the material is mostly effected by its resistivity characteristic , the piezo - resistive effect results in relatively high gauge factor or high Sensitivity. Therefore, the gaunge 'Pacton Go 4a Semiconductor strain gauge is 50 times that of the resistance Cecire) styain gauge. Gauge factor of the order of 100' to iso are also achieved by Buitable ' designs . Hence , the change in dimensions due to strain is Considered negligible in such cases. (b) Semiconductor Strain Gauge. A typical Semiconductor strain gauge is formed by the Semiconductor technology i.e., the Semiconducting coafers or filaments of length verying from 2 mm to to mm and thickness of 0.05 mm are bonded on Suitable insulating Substrates (for examples teflon). The gold leads are usually employed for making.

electrical contacts. The electrodes are formed by vapour deposition- The assembly is placed in a protective box as shown in the figure below. Semi - Conductor material Am Base Gold leads TMIITTI Electrodes. Figure : Semiconductor Strain Gauge The Strain Sensitive elements used by the Semiconductor Strain gauge are the Semiconductor materials' such as silicon and germanium. When the Strain is applied to the semiconductor element a large of change in resistance occur which can be measured with the help of a wheatstone bridge. The strain can be measured with high degree of accuracy due to relatively high change in resistance. A temperature compensated Semiconductor Strain gauge can be used to measure Small strains of the order of 10-6 ie, micro- Strain. 1. This type of gauge will have a gauge factor of 130 I 10a for a Semiconductor material of dimension 1X0.5 x 0.005 inch having the resistance of 350 12 si

(c) Advantages of Semiconductor Strain Gauge ... The gauge factor of Semiconductor strain gauge is very high. about £ 130. -2. They are useful in measurement of very small strains of the I order of 0.01 micro-strain due to their high gauges factor. .3. Semiconductor strain gauge exhibits very low hy stersi s ie, less than 0.05% .H. The Semiconductor Strain gauge has much higher output but it is as stable as a metallic strain gauge. -5. It possess a high frequency response of 1012 Hz. .6. It has a large fatigue life lię., 10 x 106 Operations can be . performed. 7. They can be manufactured in very small siges, their lengths ranging from 0.7 to 7.0mm." When this steel bar is not subjected to any load, its dimensions (L and D) remain the same. When a tensile load is applied to the bar, the bar exhibits a change in its dimensions. The tensile load acting on the bar, increase's the length of the bar. In axial direction. Due to the increases in length, the diameter of the bar decreases and thus the cross sectional area of the bar changes is, the bar exhibits' a change in its dimensions in lateral or transverse direction. Thus due to load , the bar experiences Strain in axial direction as well as in Lateral direction.

Anlal stain, El - Como eres elementos Change in diameter Lateral sbala, E., Serenal diameter Note: The negative sign before the lateral strain indicates that the diameter of the bar is decreased and ther's indicates that the bar is subjected to a tensile load. -AD i. Poisson's raliga ja A .