Downloaded from www.jayaram.com.np - More rapid than mechanical instrument. Sensor: - The device which change energy from one form to another - Depends upon the mechanical meter movement as indicating device. analysis form. - Hence have limited time response. Transducer: - Sensor which change energy from one form to electrical form. (iii) Electronics instruments:- A higher senility. Signal Condensing:Instruments: - Measurement involves the use of instruments as a physical means of determines quantities or variables. - The instrument serves as an extension of human faculties and enables the man to determine the value of unknown quantity or variable which unaided human faculty can not measure, a measuring instrument exist to provide information about the physical values of some variable being measured. - In simple cases an instrument consist of a single unit which gives an output reading or signal according to the unknown variable (measured) applied to it. - In more complex measurement situation a measuring instrument may consist of several separate elements. These separate elements may consist of traducing element which converts the measured to analogies. The analogies signal is then processed by some intermediate means and then fed to the end devices. To presents the results of the measurement for the propose of display and control. - The above mention component might be contained neither one or more boxes and the boxes holding individual measurement elements might be either close together or physically separate. - Because of this modular nature of the component contain it; it is common to refer the measuring instrument as a measurement system or instrumentation system. - The history of development of instrument encompainses three phases:(i) Mechanical Instrument:- First instrument use by man kind. - Very reliable for static and stable condition but unable to responds to dynamic and transient conditions. - having moving parts that are rigid, heavy and bulky has a large mass. (ii) Electrical Instruments:- A faster response. - A greater flexibity. - Lower weight. - Lower power consumption. (iv) A higher degree reliability.

Instrumentation System A system that comprises of input, signal, conditioning and processing and the output is known as instrumentation system. Components of Instrumentation system:Components of instrumentation system can be viewed in below diagram as:Primary seser element Trasmdure versiable conversion element variable manipulatio n element signal transducer element signal presentat ion element

Detective- x’ducer stage

Signal conditioning

Primary Sensing elements:- Measured is first detected. - It detect the physical quantity gives the output in different analogous form. - This analogues output is then converted into electrical signal by a transducer. -In many cases the physical quantity is directing converted into an electrical quantity by a treasure. -A transducer is defined as a device which converts a physical quantity into an electrical quantity.

Signal conditioning element:-

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Downloaded from www.jayaram.com.np
(I) variable conversion elements:(ii) Variable manipulation element:- Change in numerical value of signal. - Linear processes like amplification, attenuation, integration, differentiation, addition and subtraction. - Non linear process like modulation, detection sapling and filtering etc. - The element that follows primary sensing element in any instrumentation system is called system condition element. Signal transmission element:When the element of an instrument are actually physically, separated it become necessary to transmit data from one to another. The element that performs this function is called a signal transmission element. E.g. space craft. - signal conditioning and transmission stage is commonly known as intermediate stage. = (mass x acceleration) x distance (Time) = (mass x velocity/time) x distance Time = (mass x velocity) x distance (Time)2

= Mass x (length/time) x distance (Time)2 = mass x length x distance (time)2
= ML2 T3 2 -3 [P] = [ML t ]

Chapter-2

Measurement:Unit and standards of .measurement:Unit: - to specify and perform calculations with physical quantities, the physical quantities must be defined both in kind and magnitude. The standard measure of each kind of physical quantity is the unit. In science and engineering two kinds of unit:(Fundamental units:(a) Length (l) -meter (m) - [L] (b) Mass (m) -kilogram (kg) - [M] (c) Time (t) -second (s) - [T] (d) Eclectic current -Ampere (A) - [I] (e) Luminous intensity (θ) -candela (cod) - [ ]

Conversion of units:Abbreviated power of ten:Name Tera Giga Mega Kilo Hector Decal Deco Cent Mille Micro Nana Picot Tempt Atom Symbol T G M k h d d c m µ n p f a Equivalent 1012 109 106 103 102 10 10-1 10-2 10-3 10-6 10-9 10-12 10-15 10-18

(ii) Derived Units: - All other units which can be expressed in terms of fundamental unit are called derived unit. e.g. Power = work = force x distance Time (Time)

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Downloaded from www.jayaram.com.np
English into SI conversion:Question: - A frequency of signal in communication system is given as 5 MHZ express this term interim of abbreviated powers of 10 as international standard. Soln:Given frequency (f) = 5MHZ = 5 x 106 HZ Question: - A flux density in the C.G.S. system is expressed as 20 maxwells/am2. Calculate the flux density in lines/in2. (Note: - 1Maxwell=1line) B = 20 .Maxwell cm2 = 20 Maxwell x (2.54 cm /1 inch)2 x 1 line Cm2 1 maxwell = 129 lines /inch2 Question: - The velocity of light in free space is given as 2.997925 x 106 m/s express the velocity in km/hr. Question: - Calculate the velocity of a battery if a charge of 3 x 10-4 c residing on the +ve battery terminal posses 6 x 10-2 j of energy. -Not available for use outside the national laborites. - One of the main functions is the variation and calibration of secondary standards - For mass and accuracy of one part in 108 Secondary standers:- Used in industrial measuring laborites. - maintained by peritoneal involve laborites. -periodically checked by national laborites. -for mass and accuracy of one pod Working standards:⇒ Used in measurement laborites. ⇒ Used to check general laboratories instrument for their accuracy and performance. ⇒ Used in the quality control department. ⇒ For mass an accuracy of 5 PPM. And, IEEE standards:-

Standards of measurement:The term standard is applied to a piece of equipment having a known measure of physical quantity. For eg. kg, consisting of platinum iridium hollow cylinder preserved at the international bureau of weighs and measures at severs near peris asx standard of mass in SI system. There are different types of standard of measurement classified by their function and application in the following categories:(I) internal standards (ii) Primary standards (iii) Secondary standards (iv) Working standards International Standards:-Defined on the basis of international agreement. - maintained at the international al burin of weighs and measures. -Not available for the ordinary users. -Height possible accuracy. Primary Standard:- maintained by national standard laboratories.

⇒ Slightly different types of standard. ⇒ Published and maintained by the instate of electrical and electronic Engineers. ⇒ Are not physical item but the standard procedures nomenclature, definition etc. ⇒ Standard test method for testing and evaluating various electronics system and component. ⇒ Specifying of test equipment for examples seminaries in knofes and function of oscilloslscope manufacture by different manufactures., ⇒ Standard schematric and logic symbols for engineering drawing.

2.2 Measuring instrument for performance parameter:There are two types of performance parameters of means using instrument. 1. Accuracy and precision 2. Resolution and sensitivity 3. Drift 4. Static error 5. dead zone Downloaded from www.jayaram.com.np/ 3

Downloaded from www.jayaram.com.np Thus the error of 15v reading is = 15 ± 3v 1. Accuracy and precision:- Accuracy is the closeness with which an The possible % error = true value – measured value x 100% instrument reading approaches the true value of the quantity being measure True value precision specifies the repeatality of a set of reading is made independently = 15-12 x 100 with the same instrument. 15 Precision is composed of two characteristics:- conformity and the = 3 x100 number of significant digit. 15 The more significant figures, measure the greater precision of = 20% measurement. The error of meter when 82v measurement is made can still be ± 3v. Question:- A voltmeter is specified as being accurate to 1% of its full scale Then, possible % error = 82 – 79 x 100% reading, if the 100v scale is used to measure voltage of @ 12v, how 82 accurate will the reading be ? (Assuming all other error besides the meter = 3 x 100 reading error is negligible. 82 Soln:- Accuracy of meter = 1% of it’s full scale value. = 150 % = 1% of 100v =1v 41 Thus, the error of the 80v reading = 80± 1v = 3.65% The possible % error = true value – measure value x 100% Question: A set of independent voltage measurements taken by four True value observers was recovered as 117.02v, 117.11v, 117.08v and 117.03v = 80- 79 x 100 calculate the average voltage and the range of error? 80 (a) The average voltage = ≅ 1.25% (b) The range of error. n The error of the meter when the 12v measurement is made can still be ± 1v Sol :- (a) Ear = E1 + E2 + E3 + E4 Then the possible % error =12-11 *100% 4 12 = 117.06v (c) Range = Emax – Ear = ≅ 8% 1% of 100v =1v = 117.11- 117.06 = 0.05v Question:- A volt meter whose accuracy is 2% of the full scale reading is Also, used on its 0-150v scale. Voltages measured by meter are 15v and 82v. Ear – Emin = (117.06-117.02)v Calculate the possible % error of both reading. Comment upon your = 0.04v answer? ∴The average range of error = 0.05 +0.04 Soln:- Accuracy of meter = 1% of 150 4 =3 = 2 x 150 = ± 0.045 100 = ± 0.05 Downloaded from www.jayaram.com.np/ 4

Downloaded from www.jayaram.com.np Question:- Given R1 = 18.7 ohm and R2 = 3.62 ohm, then calculate, the Resolution and sensitivity:total resistance with appropriate number of significant figure if, Resolution is the smallest increament in input (the quanity being (i) R1, R2 are connected in series. measured ) which can be detected with certainly by an instrument. (ii) R1, R2 are connected in parallel. Sensitivity is defined as the ratio of the change of output to the Soln:- RT = R1 + R2 change of input. = 1807 + 3.624 Sensitivity (s) = ∆y = 22.324 ohm. (five significant figure) ∆x Since, one the resistance is accurate only three significant figure Where, ∆x = change in i/p value. Hence, ∆y = change in o/p value. RT = 22.3 ohm (3 significant figure) Deflection factor = inverse sensitivity (iii) RT = R1.R2 = ∆x R1 + R2 ∆y = 18.7 x 3.62 Question:- A wheat stone bridge require change of 7 ohm in the unknown 18.7+ 3.62 arm of the bridge to produce a change in deflection of 3mm of the = 3.03569 Ω galvanometer. Determine the sensitivity. Also determine the deflection RT = 3.03Ω (Three significant figure) factor. Soln:# Add 826± 5 to 628±3 with % error. Sensitivity = magnitude o/p response Soln:- N1 = 826 ± 5 o/p magnitude % error = 5 x 100 = 3mm 826 7Ω = ± 0.605% = 0.429 mm/Ω N2 = 625 ± 3 Deflection factor = 7/5 % error = 3 x 100% = 2.33 Ω/mm 628 Question:- A moving coil voltmeter have a scale of 100 division, the full = ± 0.477% scale reading is 250v and 1/10 of a scale division can be estimated with fair Then, degree of sentainty. Determine the resolution in volt. Sum = N1 + N2 1 scale division = 200 = 1454 ± 8 100 %error = 8 x 100% ∴Resolution = 1/10 of a scale division 1454 1 x 2v = ± 0.55% 10 Sum = 1454 ±8 (0.55%) = 0.2v Downloaded from www.jayaram.com.np/ 5

Downloaded from www.jayaram.com.np Question:- What voltage would a 20,000Ω/v meter on a 0-1-v scale show in Dade zone : It is defined as the largest change of input quantity for the circuit of figure given below:which there is no output of the instrument . (b) Dynamic characteristic: Dynamic characteristic are (1) speed of response (2) Measuring lag (3) Fidelity (4) Dynamic error Speed of response: It is defined as the rapidity with which a measuring device response to changes in the measured quantity . Measuring lag : It is the retardation or delay in the response of a measurement system to change in the measured quantity. It is of two types: (1) Retardation type :- response begins immediately after a change in measured quantity los ……………….. (2) Time delay:- response begins after a dead time after the applion of the input. (3) Fidelity:- It is defined as the degree to which a measurement system indicate changes in the measured quantity with out any dynamic error. (4) Dynamic error:- difference between true value of the quantity under measurement) changing with true. And the value indicated by measurement system if no static error is assume . It is also called measurement error. # What is the true value of voltage across the 500kilo ohm resistor connected between terminals A and B as shown in figure. What would a volt mete4r , with a sensatory of 30kilo ohm/volt read on the following ranges 50, 15, 5v when connected across terminals C and D Ans:- (10v, 8v, 5,45v, 2.86v)

Drift:- drift may be classified into three categories. (a) Zero drift o/p zero drift
Nominal characteristic

i/p o/p (b) Span drift i/p

(c) Zonal drift

Static error: It is defined as the difference between the measured value and true value of the quantity. Downloaded from www.jayaram.com.np/ 6

Downloaded from www.jayaram.com.np The Bridge said to balanced when the potential difference across the galvanometer is zero volt. So that there is no current is no current through the galvanometer. This condition occurs when VcA = VdA I1R1 = I2R2 _____________(i) If the galvanometer current is zero the following condition also exists. I1 = I3 = E ___________(ii) R1 + R3 Also, I2 = I4 = E _ ___________(iii) R2 + R4 Combining equation (i), (ii) and (iii) we get R1 = R2 R1 + R3 R2 + R4 R1(R2+ R4) = R2(R1+ R3) R1R4 = R2R3 Note:- If There of the resistance have known values 4th may be determined. Hence if R4 is the unknown resistor it’s resistance let Rx can be determine Rx = R3 R2 R4 The resistance R3 is called the standard arm of the bridge and the resistor R1 and R2 are called ratio arm.

2.3 Resistance measurement with wheat stone bridge:-

Thevenin equivalent Circuit:-

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Downloaded from www.jayaram.com.np If the galvanometer has the internal resistance Rg then, Now, the thevinin are open circuit voltage is found by (fig a) Eth Ig = Ecd = Eqc – Ead Rth + R g = I1R1 –I2R2 E E and I2 = Where, I1 = # R1 + R2 R2 + R4 Given, R1 =10 Ω R2 = 30 Ω ⎛ R1 R2 ⎞ R3 = 5 Ω ∴ E cd = Eth = E ⎜ ⎟ ⎜R +R − R −R ⎟ In the below figure. 3 2 4 ⎠ ⎝ 1

At what value of R4 will the galvanometer show the null deflection. If the bridge is balanced, find out the total current I, drawn (ii) by bridge circuit. Req 11.25 Ans:- 0.88A Question :- Fig below show the schemtic diagram of wheat stone bridge which value of bridge element as shown. The battery voltage is 5v and its internal resistance negligible. The galvanometer have a current sensitivity of 10mm per microamper and internal resistance of 10 ohm. Calculate the deflection of galvanometer caused by the 5 ohm unbalance in arm Be. (i)

And
RR R R Rth = 1 3 + 2 4 R 1 + R3 R2 + R4 Ig = Eth Rth

Ans:- Eth = 2.77mv Rth = 734Ω Downloaded from www.jayaram.com.np/ 8

Downloaded from www.jayaram.com.np Ig = 3.32 µA Rnp = (R1 / R1 + R2) Ry Similarly, Rmp = (R2/R1+R2)Ry Dethe = 33.2 mm Putting the value of Rnp and Rmp in equation (ii) we get Kelvin Bridge :⎡ ⎛ R2 ⎞ ⎤ ⎛R ⎞ ⎟ Ry ⎥ Rx + ⎜ 1 ⎟ Ry = R1 ⎢ R3 + ⎜ - Modification of wheat stone bridge ⎟ ⎜ ⎜R ⎟ ⎢ ⎝ R1 + R2 ⎠ ⎥ ⎝ 2⎠ ⎣ ⎦ - Used to measure low value resistance below 1 ohm with increased R accuracy. ∴ Rx = 1 .R3 Consider a bridge circuit given below: R2 Due to the resistance value of connecting leads of a resister (any other electrical elements)

Let, Rnp = R1 ______________(i) R2 Rmp When bridge is balanced, Rx + Rnp = R1 ( R3 +Rmp) ___________(ii) R2 Now, from equation (i) Rnp = R1 Rmp R2 Rnp + Rnp = R1 + R1 R2 + R1 Rmp +Rnp or, 2Rmp = 2R1 R1 + R2 Ry

It is necessary to connect the galvanometer G in such a way such that the bridge circuit is balance as in wheat stone bridge . This development forms the basis for construction of the Kelvin double bridge. The term “double” is used because its circuit contains a second set of ratio arm a , b as shown in figure. These arms connect the galvanometer to a point p at the appropriate potential between m and n and it elements the effect of the resistance of Ry.

An initially established condition is a = R1 Downloaded from www.jayaram.com.np/ 9

Downloaded from www.jayaram.com.np

b. R2 The ‘G’ will show the null deflection when the potential at k equals the potential at p. i.e Ekc = Elmp ________(ii) When Ekl = E x R2 R2+R1

Req of a, b, Ry =

(a + b )Ry a + b + Ry

Voltage drop in b, = I ×

(a + b )Ry a+b+ R

×

b a+b

E = R3 +

(a + b )Ry a + b + Ry

× Rx I

= I [R3 ] + Rx +

(a + b )R a + b + Ry y

Where, Ekl = E × Ekl =

⎡ (a + b )Ry ⎤ R2 × I ⎢ R3 + Rx + ⎥ __________(iii) R1 a + b + Ry ⎥ ⎢ ⎣ ⎦ Elmp = voltage drop across R3 + voltage drop across b

R2 R1 + R2

⎡ (a + b )Ry ⎤ b ∴ Eelm = I ⎢ R3 + × ⎥ a + b a + b + Ry ⎥ ⎢ ⎣ ⎦ From equation (i) and (ii) we have ⎡ (a + b )Ry ⎤ ⎡ b (a + b )R R2 I ⎢ RB + Rx + × ⎥ = I ⎢ R3 R1 + R2 ⎢ a + b + Ry ⎥ ⎢ a+b a+b+ R ⎣ ⎦ ⎣ (a + b )Ry R1 + R2 ⎡ 6 Ry ⎤ Or, R3 + Rx + = ⎢ R3 + ⎥ a + b + Ry R2 ⎢ a + b + Ry ⎥ ⎣ ⎦ (a + b )Ry R1R3 6 Ry R + R2 = + R3 + 1 × Or, R3 + Rx + R2 a + b + Ry a + b + Ry R2

⎤ ⎥ ⎥ ⎦

Rx

=

(a + b )Ry R1 6 Ry 6 Ry R1R3 R1R3 + + + − R2 R2 R2 (s + b + Ry ) a + b + Ry a + b + Ry

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Downloaded from www.jayaram.com.np Fig:- The general form of AC bridge.

2.4 A.C Bridges (inductance and Capacitance bridge):

The condition for bridge balance requires. EBA = EBC I1Z1 = I2Z2________(i) For zero detector current, (the balanced condition), the current are I1 = E Z1 + Z3 _____________(ii) E And I2 = Z2+Z1 ____________(iii) Putting the values of I1, I2 in equation (i) we get, Z1Z2 = Z2Z3 ___________(iv) Or when using admittance instead of impedance, we get. Y1Yx = y2y3 Equation (iv) is the general equation for balance of the A.C. bridge. If the impedance is written in the form Z = Z< θ Where, Z = magnitude And θ = phase angle of the complex impedance then equation (iv) can be written as:(Z< θ1) (Zx< θx) = (Z2 < θ2) (Z3< θ3) Z1Zx < θ1 θ’x Z2Z3 < θ2 θ3 Equation (v) shows that, two conditions must be simultaneously when balancing an ac bridge conditions, 1. The product of magnitude of opposite arms must be equal. i.e. Z1Zx = Z2Z3 2. The sum of the phase angle of the opposite arm must be equal. i.e. < θ1 + < θx = θ2 + < θ3 3. The impedances of the basic A.C. bridges are given as follows:Z1 = 100Ω < 800 (inductive) Z2 = 250Ω (pure resistive) Z3 400 < 30 (inductive)
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Downloaded from www.jayaram.com.np Zx = ? Z1 Determine the constants of the unknown arm if the bridge is balance = (320-j600) (200 j100) 450 Z1Zx = Z2Z3 Zx = Z2Z3 = 250 . 400 < 300 100-2 < 80 Z2 = (670.8