20151006-unit-2.pdf

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Electrical Measurements

and Instru-mentation

Dr. Sandeep Nagar

Syllabus

Galvanometer Ammeter and Voltmeters

Basic analog electronic measurements

Syllabus

Galvanometers:

Principle-Operation-Damping-Calibration-Shunts-Ballistic type

Ammeters: types-accuracy-range-Using thermocouple as ammeter-multi range ammeter-clamp on type

Voltmeters: types-accuracy-range-multi range voltmeter Transformer and their applications in the extension of instrument range

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Dr. Sandeep Nagar

Syllabus

Galvanometer

Ammeter and Voltmeters

Galvanometers

Principle Operation Damping Calibration Shunts Ballistic type

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Dr. Sandeep Nagar

Syllabus

Galvanometer

Galvanometer: Introduction

A galvanometer is an instrument used to detect presence, direction and magnitude of electric current by producing a rotating deflection of some type of pointer when electric current passes though a coil in a magnetic field.

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Dr. Sandeep Nagar

Syllabus

Galvanometer

Galvanometers: Principle

Hans Oersted discovered in 1820 that a current carrying wire deflects a magnetic needle.

This happens because time varying electric field produces magnetic field

This magnetic field interacts with magnetic field of needle and either attracts it or repels it as per the pole formation (which depend son direction of current).

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Dr. Sandeep Nagar

Syllabus

Galvanometer

Galvanometers: Principle

Deflections of coils can be used to detect and measure direction and magnitude of current.

Different ways to observe deflections:

Place a mirror on coil and shine light on mirror. When coil rotates, the image of light will move, which can be measured on a scale.

Place a marker on coil, which will produce mark on a paper.

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Dr. Sandeep Nagar

Syllabus

Galvanometer

Galvanometer: Operation

Figure:Galvanometer

Ref: https://upload.wikimedia.org/wikipedia/ commons/0/05/Galvanometer_scheme.png

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Dr. Sandeep Nagar

Syllabus

Galvanometer

Two type os galvanometers

Two types of galvanometers:

Moving magnet type:

Current is passed through a fixed coil which produces a magnetic field under which a magnet moves

Moving Coil type:

Current is passed through a movable coil placed between the poles of a powerful magnet. The coil swings under the action of a deflecting couple acting upon it

They are further divided into two types:

Weston (Pivoted Coil) d Arsonval (Suspended Coil)

Find out how Pivoted and Suspended coil type galvanometers differ and what are thier advantages and disadvantages

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Dr. Sandeep Nagar

Syllabus

Galvanometer

Galvanometers: Operation

An electric current flowing through a wire sets up a magnetic field around the wire.

The wire is wound into a coil where one end is protruded as a needle.

When current flows through the coil, one end of the coil becomes a north magnetic pole, the other a south magnetic pole.

When a permanent magnet is placed near the coil, the two fields the one from the coil and the one from the magnet interact.

The like poles will repulse each other and the unlike poles will attract.

The amount of attraction and repulsion increases as the strength of the current increases.

Direction of movement of needle will depend on direction of current.

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Dr. Sandeep Nagar

Syllabus

Galvanometer

Galvanometer: Formula

τ =B×A×I×N (1)

τ = Torque (N/m2)

B = Magnetic flux density in air gap (Wb/m2)

A = Effective coil area (m2)

N = Number of turns of wire of the coil

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Dr. Sandeep Nagar

Syllabus

Galvanometer

Galvanometer: Formula

Torque produced by current will be compensated by spring’s torque given by:

τ =Kθ (2)

K = Spring constant

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Dr. Sandeep Nagar

Syllabus

Galvanometer

Equation of motion

When currentI flows through the instrument, equation of morion can be written as:

Jd

2_θ

dt2 +D

dθ

dt +Cθ=GI (3)

Solutions of this differential equation is presented in two parts:

Particular function: representing steady state condition

Complementary function: representing transient function

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Dr. Sandeep Nagar

Syllabus

Galvanometer

Complementary fucntion

Assume that the currentI is zero, then eqn. 3 can be written as

Jd

2_θ

dt2 +D

dθ

dt +Cθ= 0 (4)

This is the condition when input current is zero i.e all deflectionsθare due to natural free vibrations of coil. The solution is of the formθ=emt

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Dr. Sandeep Nagar

Syllabus

Galvanometer

Complementary function

Jm2emt+Dmemt+Cemt = 0 (5)

Jm2+Dm+C = 0 (6)

Roots :

m1 =

−D+√D2₋₄_JC

2J (7)

m2 =

−D−√D2₋₄_JC

2J (8)

Hence the solution is:

θ=Aem1t₊_Bem2t ₍₉₎ ConstantsAandB are calculated using initial conditions.

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Dr. Sandeep Nagar

Syllabus

Galvanometer

Complementary function

For a complete solution, we have to assume the steady state condition for input i.e. currentI

For steady state current, rate of change of deflections is zero for eqn 3

Jd

2_θ

dt2 = 0 (10)

Ddθ

dt = 0 (11)

Cθ=GI (12)

θ= GI

C (13)

This gives complete solution as:

θ=Aem1t₊_Bem2t₊GI

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Dr. Sandeep Nagar

Syllabus

Galvanometer

Galvanometers: Damping

Three possible cases arise:

1 WhenD2 >4JC (non-oscillatory motion) 2 _When_D2 _<₄_JC _{(Under damped condition)}

3 _When_D2 _{= 4}_JC _{(critically damped = Dead beat)}

Solve for these conditions. For critically damped systems

m1 =m2 =

−D

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Dr. Sandeep Nagar

Syllabus

Galvanometer

Galvanometer Damping

1 Mechanical damping : Due to friction offered by

surrounding air

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Dr. Sandeep Nagar

Syllabus

Galvanometer

Galvanometer electromagnetic damping

When coil rotates in a magnetic field, due to induction effects, emf (voltage) is induced.

This results circulation of current through the coil. The current causes an opposing torque, which dampens the deflection.

An external resistor is connected to the galvanometer circuit to control the amount of current.

For a resistorRc

Rc = G

2

2√JC (15)

For derivation, see ”A course in Electronics and Electrocal Measurements and Instrumentation”, J. B. Gupta, 13th

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Dr. Sandeep Nagar

Syllabus

Galvanometer

Galvanometers: Shunts

The use of current dividers, often calledshunts, allows a meter to be calibrated to measure larger currents. A high value shunt resistor in series will limit the emf

offered to galvanometer to produce deflection. Low value shunt resistors in parallel, protect sensitive galvanometers from getting dangerous levels of currents, by providing path to current to pass majority of current through them instead of galvanometer.

But as we have seen already, this will affect the damping.

High valued resistance in series will under dampen and it will take long time to stabilize the deflection

Low valued resistance in parallel will over damp the galvanometer and it will become sluggish.

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Dr. Sandeep Nagar

Syllabus

Galvanometer

Galvanometers: Ballistic type

A special feature of ballistic galvanometers is that its rotating coil has a large moment of inertia.

It is used to measure quantity of chargerather than currents

The passage of the charge produces an impulse, a momentary torque, which causes the coil then to swing slowly to some maximum position

Mathematically, its is an integrator which measures the quantity of charge discharged through it over a period of time

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Dr. Sandeep Nagar

Syllabus

Galvanometer

Galvanometers: Calibration

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Dr. Sandeep Nagar

Syllabus

Galvanometer

Electrical meters

Voltmeter, Ammeter and Ohm-meter’s design starts with a current sensitive element.

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Dr. Sandeep Nagar

Syllabus

Galvanometer

Changing galvanometer to other meters

Figure:Changing galvanometer to other meter

Ref: http://hyperphysics.phy-astr.gsu.edu/hbase/ magnetic/movcoil.html

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Dr. Sandeep Nagar

Syllabus Galvanometer

Ammeters and Voltmeters

Types Accuracy Range

Using thermocouple as ammeter/voltmeter Multi range ammeter/voltmeter

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Dr. Sandeep Nagar

Ammeter- Types

Moving iron type

1 _{Attraction type} 2 _{Repulsion type}

Moving coil type

1 _{PMMC (Permanant magnet moving coil)} 2 _{DMC (Dynamometer type moving coil)}

Thermal type

1 _{Hot wire} 2 _Thermocouple

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Dr. Sandeep Nagar

Moving iron type ammeter

Coil carries the current and it produces a magnetic field. Magnetic field either attracts or repels two iron bars, which eventually align themselves in the direction of magnetic field.

Marker on bar magnet can record the displacement Displacement is proportional to amount of current More detailed description at see ”A course in Electronics and Electrical Measurements and Instrumentation”, J. B. Gupta, 13th Edition, Page = 234−253

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Dr. Sandeep Nagar

Moving coil type ammeter

PMMC:

Same as PMMC galvanometer with a shunt resistance Value of shunt resistance provides various ranges

DMC:

Same as PMMC except permanent magnet is replaced by two fixed air-cored coils

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Dr. Sandeep Nagar

Hot wire ammeters

Metals with higher temperature coefficient of expansion are used

When current passes through them, they expand

This displacement/deflection can be recorded by a marker A Pt-Ir alloy is used for the wires

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Dr. Sandeep Nagar

Thermocouple based ammeters

Thermoemf (generated due to Seebeck effect) is

measured, which is generated by the heating of element due to passage of current

Either the hot junction is close to current carrying wire, or close to it (in which case hot junction is heated via radiation phenomenon)

Governing equation:

e =α(T −T0) +

1 2β(T

2₋_T2 0)

Where:

e = Thermoemf

T = Absolute temperature of hot junction

T0 = Absolute temperature of cold junction α andβ are material constants

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Dr. Sandeep Nagar

Rectifyer type voltmeter

Current rating of a diode is very important to note before using it to make a rectifier circuit

Si diodes have current rating until 500mAand voltage

rating until 1000V whereas Ge diodes have 100mAand

300V respectively.

Diodes are arranged in wheatstone bridge configuration and galvanometer is attached between one set of extreme ends to measure whereas signal is fed at other two. More detailed description at: ”A course in Electronics and Electrical Measurements and Instrumentation”, J. B. Gupta, 13th Edition, Page = 279−283

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Dr. Sandeep Nagar

Transformer and their applications in the extension

of instrument range

Transformers are used to extend the range of measurement using moderately sized and capacity instrument

Two kinds:

Current/series transformers

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Dr. Sandeep Nagar