INSTRUMENTATION & MEASUREMENTS(EE-302)

WEEK 2

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Derived Units

Units other than fundamental and supplementary are derived from the fundamental and supplementary units and are primarily classified into:

Mechanical Units like mass, velocity, acceleration, force, weight, torque, work, energy, power etc.

Electric and Magnetic Units such as power, energy, ohms, farads, henries, magnetic flux in webers, tesla etc.

Thermal Units such as latent heat specific heat capacity, sensible heat, calorific value etc.

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Problems

A set of solved problems related to Units shall be provided soon.

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Bridge Measurements

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Bridge Circuits & their importance

Used not only for measurement of resistance but also used for the measurement of capacitance and inductance.

In simplest form it consists of four arms network.

They use Comparison measurement technique and null-indication principle.

Unknown component’s value is calculated when the bridge is balanced.

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Advantages of Bridge Circuits

Balance equation independent of the magnitude of the input voltage or the source impedance.

High measurement accuracy since measurement is based upon comparison.

Accuracy depends upon component values and not on the characteristics of the null detector.

Balance equation is independent of the sensitivity of the null detector.

Balance condition transparent to the interchange of source and detector positions.

Can be used in the control circuits.

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Types of Bridges

DC bridges

AC bridges

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DC bridges

Wheatstone Bridge

Kelvin Bridge

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AC Bridges

Capacitance comparison bridge

Inductance comparison bridge

Maxwell’s Bridge

Hay’s Bridge

Anderson Bridge

Schering Bridge

Wien Bridge

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Wheatstone Bridge

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R1 and R2 are called the ratio arms.

R3 is called the standard arm containing the standard known resistance.

R4 is the unknown resistance to be measured.

Battery connected between A and C.

Galvanometer attached between B and D.

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Wheatstone Bridge

The balanced condition is defined by a condition when the galvanometer shows ZERO current through it.

This bridge works on the principle of null deflection or null indication.

For zero current through the galvanometer, B and D must be at the same potential.

Thus potential AB should be equal to the potential AD.

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Wheatstone Bridge

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Wheatstone Bridge

Thus R4=R3 R1/R2, and this is the required balanced condition of this bridge.

Depends upon the ratio of R1 and R2, hence the arms are called ratio arms.

Based upon Null indication, hence results are not dependant upon the calibration characteristics of the galvanometer.

R3 could be varied to get the required resistance.

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Wheatstone Bridge

Industrial Form of the Wheatstone Bridge

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Sensitivity of Wheatstone bridge

When the Wheatstone bridge is not balanced, a certain amount of current flows through the galvanometer that depends upon the sensitivity of the galvanometer.

This is given by:

Sensitivity S=deflection D/current I (mm/µA, radians/µA or degrees/µA)

Greater the sensitivity of the galvanometer, greater its deflection.

Another means of defining sensitivity of the galvanometer is the amount of deflection per unit voltage across the galvanometer means:

Sv=θ/e, where ‘e’ is the voltage across the galvanometer and ‘θ’ is the deflection of the galvanometer.

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The bridge sensitivity can also be defined as the deflection of the galvanometer per unit fractional change in the unknown resistance. This is called SB defined by:

SB = θ/(∆𝑅

𝑅)

Here ∆𝑅/𝑅is unit fractional change in unknown resistance.

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Sensitivity of Wheatstone bridge

Wheatstone bridge under small Unbalance At the balance condition, 𝑅4 = 𝑅3

𝑅1

𝑅2, this means

𝑅4/𝑅3 = 𝑅1/𝑅2.

Under the unbalanced condition the bridge would look like:

Here ∆𝑅 is creating

The unbalance.

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Wheatstone bridge under small Unbalance

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Wheatstone bridge under small Unbalance

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Wheatstone bridge under small Unbalance

Thevenin’s Equivalent & Galvanometer Current

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Thevenin’s Equivalent & Galvanometer Current

Galvanometer current under Unbalanced Condition

For such a case, various relationships are given below:

VTH = ERΔR/4R2 = EΔR/4R

Req = R2/2R + R2/2R = R

and subsequently

Ig = EΔR/4R/R+Rg = E (ΔR/4R)/R+Rg

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Measurement Errors

Very precise reference resistances are required to properly balance the Wheatstone bridge.

Insufficient efficiency of the null detector might cause error.

Resistance variations due to the heating effect.

Low value resistance measurement problems due to the Thermal emf.

Contact/Leads resistances exterior to the bridge might cause errors.

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Applications of the Wheatstone bridge

Measurement of various DC resistances of wires for quality control.

Measurement of motor winding resistance, relay coils etc.

Used by telephone companies to detect underground cable faults.

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Advantages of the Wheatstone bridge

Null Detection mechanism ensures accurate results.

Source fluctuations do not hamper readings.

Accuracy and sensitivity higher than direct reflection meters.

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Limitations of the Wheatstone bridge

Effect of lead and contact resistance becomes significant while measuring small resistances.

Cannot be used to measure resistances in the mega ohms range, this happens because of the high resistance presented by the bridge and the inability of the galvanometer to show any imbalance.

Heating effect as a result of current may permanently damage the resistors.

Used resistances must be very precise with 1% or 0.1%that costs high.

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Example

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Example 2

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Example 2-Solution

Kelvin bridge

Low resistances can not be accurately measured by the Wheatstone bridge due inaccuracies caused by the lead and contact resistances.

For low resistance measurement (below 1Ω) Kelvin bridge is used.

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Kelvin bridge

Ry represents the resistance of the connecting leads from R3 to Rx.

Rx is the unknown resistance to be measured.

Galvanometer could be connected either at ‘a’, ‘b’ or ‘c’ positions.

If the galvanometer is connected to ‘a’ , the lead resistance Ry added to Rx. If the galvanometer is connected to ‘c’, then Ry gets added to R3.

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Kelvin bridge

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Kelvin bridge

Kelvin bridge

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Double Kelvin’s bridge

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Kelvin Double bridge

Contains a second arm with resistances ‘a’ and ‘b’. With these resistances the galvanometer is connected to point 3.

Galvanometer gives null deflection when the potential of the terminal 3 is the same as that of the potential of the terminal 4.

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The equivalent circuit when the galvanometer is carrying zero current i.e the balanced condition is shown below:

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Then balance equation for the bridge is:Rx = R1 R3/R2

Bridge in Control Circuits

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Parameter sensitive resistance generates the error signal which could be used for the control purposes. This mechanism is the same for a number of bridge based error generation scenarios.

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AC Bridges

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Sources & Detectors

At very low frequencies, the power line itself can act as source of supply.

For high frequencies, electronic oscillators are used as supply.

A typical oscillator has a range of 50 Hz to 125kHz with a power output of around 7 W.

Common detectors for AC bridges are Headphones, Vibration galvanometers and Tunable amplifier detectors.

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Headphones: from 250 Hz upto 4kHz.

Vibration Galvanometers: low audio frequencies 5 Hz to 1000 Hz.

Tunable amplifier detectors: 10 Hz to 100 kHz.

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Bridge balance equations

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The summary….

THE PRODUCTS OF THE MAGNITUDES OF THE OPPOSITE ARMS MUST BE EQUAL WHILE SUM OF THE PHASE ANGLES OF THE OPPOSITE ARMS MUST BE EQUAL.

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