MODULE 2 POTENTIOMETERS AND BRIDGEStijubaby.weebly.com/uploads/4/3/6/9/4369784/module_5...Rectangular type ( Co-ordinate type) ac potentiometer •Developed by D.C Gall – Gall co-ordinate

MODULE VAC AND DC POTENTIOMETERS

BRIDGESAND CRO

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Potentiometers

• General Principle • DC potentiometer

– Slide wire – Crompton – Multi range Applications

• AC potentiometer – Gall Tinsley – Drysdale Applications

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What is a potentiometer?

• This is a very basic instrument used for comparing emf two cells and for calibrating ammeter, voltmeter and watt-meter.

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General Principle of potentiometer

• Suppose we have connected two batteries in head to head and tale to tale through a galvanometer.

• That means the positive terminals of both batteries are connected together and negative terminals are also connected together through a galvanometer as shown in the figure

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• If the voltage of both battery cells is exactly equal, there will be no circulating current in the circuit and hence the galvanometer shows null deflection.

• The working principle of potentiometer depends upon this phenomenon.

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Basic of slide wire potentiometer

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Basic of slide wire potentiometer(contd…)

• Think about a circuit, where a battery is connected across a resistor via a switch and a rheostat as shown in the figure, there will be a voltage drop across the resistor.

• As there is a voltage drop across the resistor, this portion of the circuit can be considered as a voltage source for other external circuits.

• That means anything connected across the resistor will get voltage.

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http://www.electrical4u.com/voltage-or-electric-potential-difference/


• If the resistor has uniform cross section throughout its length, the electrical resistance per unit length of the resistor is also uniform throughout its length.

• Hence, voltage drop per unit length of the resistor is also uniform.

• Suppose the electric current through the resistor is i A and resistance per unit length of the resistor is r Ω.

• Then the voltage appears per unit length across the resistor would be 'ir' ans say it is v volt.

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• Now, positive terminal of a standard cell is connected to point A on the sliding resistor and negative terminal of the same is connected with a galvanometer.

• Other end of the galvanometer is in contact with the resistor via a sliding contact as shown in the figure above.

• By adjusting this sliding end, a point like B is found where, there is no current through the galvanometer, hence no deflection of galvanometer.

• That means emf of the standard cell is just balanced by the voltage drop appears across AB.

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• Now if the distance between point A and B is L, then it can be written emf of standard cell E = Lv volt.

• As v (voltage drop per unit length of the sliding resistor) is known and L is measured from the scale attached to the resistor, the value of E i.e. emf of standard cell can also be calculated from the above simple equation very easily.

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Principle of of slide wire potentiometer

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Principle of of slide wire potentiometer(contd…)

• Two cells whose emf's are to be compared are joined as shown in the figure below.

• The positive terminals of the cells and source battery are joined together.

• The negative terminals of the cells are joined with the galvanometer in turn through a two way switch.

• The other end of the galvanometer is connected to a sliding contact on the resistor.

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• By adjusting sliding contact on the resistor, it is found that the null deflection of galvanometer comes for first cell at a length of L on the scale and after positioning to way switch to second cell and then by adjusting the sliding contact, it is found that the null deflection of galvanometer comes for that cell at a length of L1 on the scale.

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• Let's think of the first cell as standard cell and it's emf is E and second cell is unknown cell whose emf is E1.

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CROMPTON DC POTENTIOMETER-Not included in syllabus but just read it...!

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• Draw back of slide wire potentiometer is that its accuracy depends on uniformity of the wire

• Crompton dc potentiometer is a modified form of slide wire potentiometer where calibrated slide resistors with a small circular wire of one or more turns thus reducing the size of the equipment

• The effect of very long slide wire is obtained by connecting a number of resistance coils in series with a comparatively short wire




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• AB- graduated slide wire having resistance 10Ω

• PA- resistance coils each having resistance of

slide wire

• C1- slide moving over PA

• C2- slide moving over AB

• R1- coarse adjustment

• R2- fine adjustment

• E1- supply voltage




• SD- double throw switch used to toggle betwenn standardization and measurement of unknown emf

• S1,S2- single throw switch

• G- galvanometer

• E2- standard cell used for standardization

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• Standardization: – Galvanometer is heavily shunted

– Potentiometer is stanrdized by putting SD switch in calibrate position

– For this Wetson type standard cell (1.0183V) is used

– For this slide C2 is set on stud 1 and C1 is set on .0183

– Now R1 and R2 are adjusted to get zero deflection on the galvanometer

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CROMPTON DC POTENTIOMETER Working -Not included in syllabus but just read it...!

• Measurement of unknown emf

– Switch S2 is closed

– SD is kept at operate position

– R1 and R2 is kept fixed as in standardized position

– Now unknown emf is connected to SD

– Slide contacts C1 and C2 are adjusted to obtain balance of the potentiometer

– At balance reading of the potentiometer directly gives the value of unknown emf

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CROMPTON DC POTENTIOMETER

Disadvantages -Not included in syllabus but just read it...!

• It is not possible to arrange sliding contacts C1 and C2 to coincide to exact reading

• Before making measurement current has to be allowed to flow through the potentiometer.

• If balancing takes longer, then standardization has to be checked

• Standardization has to be checked each time while measuring unknown emf.

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APPLICATIONS OF DC Potentiometers 1) Calibration of voltmeter

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Potential difference measured on the potentiometer multiplied by the ratio of Voltage Ratio box gives the actual pd across the voltmeter

Voltage across the voltmeter is changed by changing the position of sliding contact on potential divider and process is repeated for various values



APPLICATIONS OF DC Potentiometers 2) Calibration of Ammeter

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Voltage drop across Rs is measured by potentio meterVoltage drop divided by Rs is current through AmmeterBy varying value of Rs,ammeter can be calibrated



APPLICATIONS OF DC Potentiometers 3) Calibration of Wattmeter

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std resistance used to calibrate current coil

VR box used to calibrate potential coil



AC potentiometers

• The principle of a.c potentiometer is the same as that of the d.c potentiometer.

• The most important difference between d.c and a.c potentiometer is that in d.c potentiometer only the magnitude of the unknown emf and potentiometer voltage drop have to be made equal to obtain balance.

• In a.c potentiometer both magnitude and phase of two have to be same to obtain balance.

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AC potentiometers

The basic requirement for the operation.

• Equality of voltage being compared at all instant these require equal phase and magnitude at all instants.

• In other words the frequency and waveform of the current in the potentiometer circuit must be same as the voltage measured.

• A vibrational galvanometer is usually used as a detector in a a.c potentiometer it is a tuned device ie, responding to one frequency in presence of harmonics balance may never be achieved only a minimum deflection point is achieved.

• Stray emf picked up from stray fields or coupling between portions of the potentiometer circuit seriously affect the result.

• Imperfect standardisation procedure which contributes to an error

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Types of AC potentiometers

• Polar Type

• Coordinate type

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Polar type ac potentiometer

• The magnitude of the unknown voltage is read from one scale and its phase angle, with respect to some reference phasor,is read directly from the second scale

• Provision is made to read phase angle between 0 to 360 degrees

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Polar type ac potentiometer (Drysdale polar potentiometer)

• This type of potentiometer measures unknown emf in polar form that is in terms of its relative magnitude and phase

• Unknown emf is balanced by means of single voltage ( reference voltage or standard voltage)which is continuously variable in both magnitude and phase

• Developed by Dr. C V Drysdale

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Drysdale polar potentiometer

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Rectangular type ( Cordinate type) ac potentiometer

• It measures unknown emf in terms of its regular cordinates

• Balance is obtained by two voltages which are in quadrature (having phase difference of 900)

• Each of these voltages is varied in magnitude and a phase splitter is used to check the quadrature

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Rectangular type ( Co-ordinate type) ac potentiometer

• Developed by D.C Gall – Gall co-ordinate potentiometer

• Designed by H.Tinsley and Co.

• So Rectangular type ac poentiometer is known as Gall Tinsley potentiometer

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Gall Tinsley co-ordinate potentiometer

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APPLICATIONS OF AC POTENTIOMETERS

• Calibration of Voltmeter

• Calibration of Ammeter

• Calibration of Energymeter

• Finding of self Inductance

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BRIDGES

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What is Bridge circuit?

• A bridge circuit is a type of electrical circuit in which two circuit branches (usually in parallel with each other) are "bridged" by a third branch connected between the first two branches at some intermediate point along them.

• The bridge was originally developed for laboratory measurement purposes and one of the intermediate bridging points is often adjustable when so used.

• Bridge circuits now find many applications, both linear and non-linear, including in instrumentation, filtering and power conversion.

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http://en.wikipedia.org/wiki/Electrical_circuit



http://en.wikipedia.org/wiki/Instrumentation

http://en.wikipedia.org/wiki/Electronic_filter

http://en.wikipedia.org/wiki/Power_converter

BRIDGE CIRCUITS

• DC Bridges – Wheatstone’s bridge

– Kelvin’s Double Bridge

– PO box

• AC Bridges – Maxwell’s bridge

– Scherig Bridge

– Anderson Bridge

– Wien’s Bridge

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Examples of Bridge circuit

• the Wheatstone bridge, was invented by Samuel Hunter Christie and popularized by Charles Wheatstone, and is used for measuring resistance.

• It is constructed from four resistors, two of known values R1 and R3 (see diagram), one whose resistance is to be determined Rx, and one which is variable and calibrated R2.

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http://en.wikipedia.org/wiki/Wheatstone_bridge

http://en.wikipedia.org/wiki/Samuel_Hunter_Christie

http://en.wikipedia.org/wiki/Samuel_Hunter_Christie

http://en.wikipedia.org/wiki/Charles_Wheatstone

http://en.wikipedia.org/wiki/Electrical_resistance

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AC Bridges

– Maxwell’s bridge

– Scherig Bridge

– Anderson Bridge

– Wien’s Bridge

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AC BRIDGES

• AC Bridges consist of a source, balance detector and four arms.

• In AC bridges, all the four arms consists of impedance.

• The AC bridges are formed by replacing the DC battery with an AC source and galvanometer by detector of Wheatstone bridge.

• They are highly useful to find out inductance, capacitance, storage factor, dissipation factor etc.

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http://www.electrical4u.com/battery-history-and-working-principle-of-batteries/

http://www.electrical4u.com/wheatstone-bridge-circuit-theory-and-principle/

BASIC PRINCIPLE OF AC BRIDGES

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• Here Z1, Z2, Z3 and Z4 are the arms of the bridge.

• Balance condition, the potential difference between b and d must be zero.

• From this, when the voltage drop from from a to d equals to drop from a to b both in magnitude and phase

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• Under balanced condition,

𝐼1 = 𝐼3

𝐼2 = 𝐼4

𝐼1 = 𝑒

𝑍1 + 𝑍3

𝐼2 =𝑒

𝑍2 + 𝑍4

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BASIC PRINCIPLE OF AC BRIDGES (contd…)

• 𝑉𝑏 = 𝐼3𝑍3

• 𝑉𝑑 = 𝐼4𝑍4

• Under balanced condition

𝑉𝑏 = 𝑉𝑑

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BASIC PRINCIPLE OF AC BRIDGES (contd…)

• Under balance,

• Hence, 𝑍1𝑍4 = 𝑍2𝑍3

𝑒𝑍3

𝑍1 + 𝑍3=

𝑒𝑍4

𝑍2 + 𝑍4

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Conclusion

• Following are the important conclusions that can be drawn from the above equations:

(a) We get two balanced equations that are obtained by equating real and imaginary parts this means that for an ac bridge both the relation (i.e. magnitude and phase) must be satisfied at the same time. Both the equations are said to be independent if and only if both equation contain single variable element. This variable can be inductor or resistor. (b) The above equations are independent of frequency that means we do not require exact frequency of the source voltage and also the applied source voltage waveform need not to be perfectly sinusoidal.

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Maxwell’s Bridge

• Maxwell’s inductance Bridge

• Maxwell’s inductance capacitance Bridge ( Maxwell Wien Bridge)

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Maxwell’s Inductance Bridge

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Maxwell’s Inductance Bridge(contd..)

• 𝐼1 =𝑒

𝑟1+𝑟3+𝑗𝛚𝑙1

• 𝐼2 =𝑒

𝑟2+𝑟4+𝑗𝛚𝑙2

• 𝑉𝑏 = 𝐼1𝑟3

• 𝑉𝑑 = 𝐼2𝑟4

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• Under balanced condition,

• 𝑉𝑏 = 𝑉𝑑

𝑒

𝑟1+𝑟3+𝑗𝛚𝑙1𝑟3=

𝑒

𝑟2+𝑟4+𝑗𝛚𝑙2𝑟4

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• 𝑟3𝑟4 + 𝑟3𝑟2 + 𝑗𝛚𝑙2𝑟3

= 𝑟4𝑟1+ 𝑟4𝑟3+𝑗𝛚𝑙1𝑟4

By equating real and imaginary parts,

𝑟1= 𝑟3𝑟2

𝑟4

𝑙1= 𝑙2𝑟3

𝑟4

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Maxwell’s Inductance Bridge(contd..) Phasor Diagram

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Maxwell Wien Bridge (Maxwell's Inductance Capacitance Bridge)

• In this Maxwell Bridge, the unknown inductance is measured by the standard variable capacitor.

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• 𝑍1 = 𝑟1 + 𝑗𝛚𝑙1

• 𝑍2 = 𝑟2

• 𝑍3 = 𝑅3

• 𝑍4 =𝑟4(−𝑗/𝛚𝐶4) 𝑟4−(𝑗/𝛚𝐶4)

= −𝑗𝑟4

𝛚𝐶4𝑟4 − 𝑗

= 𝑟4

𝑗𝛚𝐶4𝑟4 + 1

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• Under balance,

𝑍1𝑍4 = 𝑍2𝑍3

• (𝑟1+𝑗𝛚𝑙1) (𝑟4

𝑗𝛚𝐶4𝑟4+1)

=𝑟2𝑅3

Ie

𝑟1𝑟4+𝑗𝛚𝑙1𝑟4 = 𝑗𝛚𝐶4𝑟4𝑟2𝑅3+𝑟2𝑅3

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Equating real and imaginary parts

𝑟1𝑟4=𝑟2𝑅3

𝑟1=𝑟2𝑅3

𝑟4

𝑙1=𝐶4𝑟2𝑅3

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Problem

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Scherig Bridge

• This bridge is used to measure to the capacitance of the capacitor, dissipation factor and measurement of relative permittivity.

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Scherig Bridge(contd…)

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• C 1 is the unknown capacitance whose value is to be determined with series electrical resistance r1.

• c2 is a standard capacitor. • c4 is a variable capacitor. • r3 is a pure resistor (i.e. non

inductive in nature). • r4 is a variable non inductive

resistor connected in parallel with variable capacitor c4.

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• Now the supply is given to the bridge between the points a and c.

• The detector is connected between b and d.

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• at balance condition, 𝑍1𝑍4 = 𝑍2𝑍3

𝑍1=

𝑍2= 1

𝑗𝛚𝐶2

𝑍3= 𝑟3

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• 𝑍4 =𝑟4(−𝑗/𝛚𝐶4)

𝑟4−𝑗/𝛚𝐶4

= −𝑗𝑟4

𝛚𝐶4𝑟4−𝑗

=𝑟4

𝑗𝛚𝐶4𝑟4 + 1

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Scherig Bridge(contd…) Phasor diagram

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• Dissipation factor

• To find permitivity find the area and lengrth of capacitor c1.

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Wien’s Bridge

• Wien’s Series bridge

• Wien’s parallel bridge

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Wien’s parallel bridge Bridge (R3 parallel to C3)

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Wien’s parallel Bridge(contd..)

• Wien Bridge has a series RC combination in one and a parallel combination in the adjoining arm.

• Its basic form is designed to measure frequency.

• It can also be used for the instrument of an unknown capacitor with great accuracy.

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• 𝑍1 = 𝑅1 −𝑗

𝛚𝐶1

• 𝑍2 = 𝑅2

• 𝑍3 =𝑅3

1+𝑗𝛚𝐶3𝑅3

• 𝑍4 = 𝑅4

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Wien’s Bridge(contd..)

• At balance condition 𝑍1𝑍4 = 𝑍2𝑍3

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Wien’s Bridge(contd..)

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• The bridge is used for measuring frequency in the audio range. Resistances R1 and R3 can be ganged together to have identical values. Capacitors C1 and C3 are normally of fixed values.

• The audio range is normally divided into 20 - 200 - 2 k - 20 kHz range. In this case, the resistances can be used for range changing and capacitors, and C3 for fine frequency control within the range.

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• The bridge can also be use for measuring capacitance. In that case, the frequency of operation must be known.

• The bridge is also used in a harmonic distortion analyzer, as a Notch filter, an in audio frequency and radio frequency oscillators as a frequency determine element.

• An accuracy of 0.5% - 1% can be readily obtained using this bridge. Because it is frequency sensitive, it is difficult to balance unless the waveform of the applied voltage is purely sinusoidal.

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Wien’s series bridge

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Types of detectors used in ac bridges

Frequency range Detector used

Low frequency Vibration Galvanometer A moving coil galvanometer has a range of 1.5kHz

Lab networks frequencies upto 100Hz Moving coil type instrument which has high sensitivity

Higher frequencies(>800Hz) Telephone(headphone)

Above 3kHz Heterodyne or beat tone detector

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Documents

MODULE 2 POTENTIOMETERS AND BRIDGEStijubaby.weebly.com/uploads/4/3/6/9/4369784/module_5...Rectangular type ( Co-ordinate type) ac potentiometer •Developed by D.C Gall – Gall co-ordinate