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1. A resistor has oltage drop of 110.V and current of.a. the uncertainties in the measurement of oltage and current are ± 0.V and ±0.01 respectiely calculate the uncertainty in power calculation. Ans. Power (P) oltage x current V x I 110.. 606.1 w P + i P w w () i V I Where w and wi are uncertainties in calculation of oltage and current respectiely. P VI I. V V ( ii) P VI V 110. I I ( iii) By i, ii, iii. 0. + 110. 0.01 ±.96 w.96 100 0.888% 606.1. A PMMC oltage has a reading of 9V when it is measuring a oltage source with an internal resistance of finite alue on its scale of 10V. When scale of this is changed to 0 full scale then reading of 13 is obtained. Gien sensitiity of oltmeter to be 0 kω/v. Find alue of the oltage source and its internal resistance R. Ans. VV oltage across oltmeter Rs Vs R + R s...( i) Vs oltage of source Rs and R are resistance of source & oltmeter respectiely. Case i V 9V, Vs? Rs? RV sensitiity range 0 k Ω / V 10 00 k/ω by (1) 9 VsR R s + 00 9 (Rs + 00) VsR Vs. (00) 9 (Rs + 00) Case ii VV 13V VS? RS? RV 0kΩ / V 0 RV 1000 kω by (1) Vs R 13 ( R + 1000) s Vs (1000) 1. (Rs + 1000)...(iii) by (ii) & (iii) 9( Rs + 00) 13( Rs + 1000) 00 1000 18 Rs + 9000 13 Rs + 13000 S0 Rs 000 Rs 800...(ii) 3. Gien a meter of range 0 1mA, haing internal resistance of Ω. How do you extend the range of it to 10 ma? Ans. To extend the range of ammeter a shunt resistance is applied to ammeter to bypass excess current through this shunt resistor. Only rated current flours through ammeter. But now the dial of ammeter has to be recalibrated by multiplying the alues with multiplication factor m. by following aboe steps the range of ammeter is extended. Numerical :
Rm internal meter resistance Rsh external shunt resistor to bypass excess current Im meter current Ish current in shunt arm I rated current of extended range meter V Im Rm IshRsh [KVL] Im Rm [I Im] Rsh ( I Im + Ish KCL) R sh Rm I wherem ( m 1) Im m multiplication factor I 10mA, Im 1 ma, Rm Ω, I m 10 I m Rsh 10 1 Rsh 0. 9 So, by connecting shunt resistance of 0.6Ω and multiplying dial alue by m 10 the range of ammeter will be extended from 1 ma to 10 ma.. A) explain the following terms with respect to measurement system:- i) accuracy ii) precision iii) resolution i) sensitiity ) linearity B) A oltmeter is connected across 10kΩ resistor as shown in figure The oltmeter shows., but it must hae shown V. Why is his happening? Explain Ans. i) Accuracy: The closeness with which instrument alue or reading approaches the true alue or quantity being measured. It means conformity to truth. ii) Precision: It is measure of reproducibity of the measurements precision is a measure of degree of agreement within a group of measurements. iii) Resolution: The smallest increment in the quantity being measured that can be measured with certainty by an instrument. i) Sensitiity: sensitiity of an instrument is ratio of magnitude of output signal / response to the magnitude of input signal / quantity being measured. ) linearity: linearity is simply measure of maximum deiation of calibration points from the straight line. B) The reduction in measured alue of oltmeter is due to loading effect to oltmeter as oltmeter has some finite input resistance Had the internal resistance of oltmeter infinite then no loading effect will occur and alue shown by oltmeter will be true alue itself Let RV be internal resistance of oltmeter So, RV is parallel to 10kΩ resistance and is uialent Resistance 10R R e 10 q R k 10 + R oltage shown by oltmeter 0 ( KVL) R + 10K 0. R + 10. + 0 9.60k. R 9.60k 10R 9.60 10 + R 3
10R 96 + 9.6 R 0. R 96 96 R 0k 0. Therefore R 0k and this resistance of oltmeter causes the net oltage to reduce and is called loading effect. Define gauge factor for strain gauge and derie the expression for the same. Also explain the significance of piezo resistiity in the expression. Ans. If a metal is stretched or compressed, its resistance changes on account of fact that both the length and diameter / area of conductor changes. Also there is change in alue of resistiity when strained. Gauge factor deriation: Consider a wise haing initial length L and diameter D when stress or force is applied its length increases by ΔL and diameter decreases to D L Resis tance R A resistiity L length of wire D A area of wire D diameter of wire L R A ln R ln + ln(l) ln(a) () i [taking natural log both sides] differentiate the aboe uation with respect to stress (σ) 1 dr 1 d 1 dl 1 da + R d d L d A d D A da ( D) dd D dd d d d 1 da D dd dd A d D d D d 1 da dd A d D d...( iii) by (ii) & (iii) 1 R 1 d 1 dl dd + R d d L d D d ( ii) Rearranging aboe uation for small ariation:- dr d dl dd + R L D R L D + R L D R / R D / D / 1 + L / L L / L L / L R/ R D/ D / Guage factor 1 +... L / L L / L L / L D D poissons ratio L L R / R P / P Guage factor 1+ + L / L L / L for resistor made of metal resistiity is not changed so gauge factor depends on GF (1+ ) dimensions For resistor mode of semiconductors so guage factor depends mainly on / L/ L sharply.. As resistiity changes