Study notes on A.C Bridges & Potentiometer For Electrical Engineering

AC Bridges

AC bridges are fundamental tools in electrical engineering used for precise measurement and analysis of resistive, capacitive, and inductive components in AC circuits. These bridges provide a balanced condition where unknown elements are compared against known reference elements. By achieving balance, AC bridges allow for the accurate determination of component values, making them indispensable in fields such as electronics, telecommunications, and metrology.

Types of Sources

1. At low frequencies, a power line is used as a source.
2. At high frequencies, electronic oscillators are used as a source

Types of Detectors

1. Vibration galvanometer at low power frequency and audio frequency (up to 1000 Hz)
2. Headphones at an audio frequency (250 Hz to 4 kHz)
3. Tuneable amplifier for frequency range (10 Hz to 100 kHz)

General Bridge Circuit

At balanced bridge 

Magnitude condition 

Angle condition 

For a balanced bridge both the magnitude

Measurement of Self Inductance

• Maxwell’s inductance bridge
• Maxwell’s inductance-capacitance bridge
• Hay’s bridge
• Anderson’s bridge
• Owner's bridge

Maxwell’s Inductance Bridge

Maxwell's Inductance Bridge is a measurement technique developed by James Clerk Maxwell, the renowned physicist and mathematician. It is a variation of the Wheatstone bridge and is specifically designed for the precise measurement of inductance. By balancing the unknown inductance with known values, Maxwell's Inductance Bridge enables accurate determination of inductance in electrical circuits, making it a valuable tool in electrical engineering and scientific research.

Where, L1 = Unknown inductance of resistance R1

L2 = Variable induactance

R2 = Standard variable resistance

R3, R4 = Fixed non-inductance resistance

Maxwell’s Inductance - Capacitance Bridge

Q-factor, 

Q-factor range 1 < Q < 10, for medium Q-coils

Where, R4 = Variable non-inductive resistance

C4 = Standard variable capacitance

Note: If C4 is fixed, then a balanced bridge is obtained as

• Either by varying R2 and R4.
• Put a resistance in series with L1 and varying R4.

Hay’s Bridge

Where, C4 = Standard capacitance

Q-factor 

for Q > 10 i.e., high Q-coils

L1 = R2R3C4

Anderson’s Bridge

Where, L1 = Unknown self-inductance with an internal resistance R1

R2, R3, R4 = Fixed standard non-inductive resistance

r = A variable resistance

C = A fixed capacitance

• Anderson’s bridge is suitable for small Q-factor i.e., Q < 1.
• It can also be used for the measurement of capacitance in terms of inductance.

Key Points

• Maxwll’s bridge is used to measure the inductance of a low Q-inductor.
• Hay bridge is used to measure the inductance of a high Q-inductor.
• Inductance is measured in terms of capacitance, resistance by Anderson’s bridge.

Owen’s Bridge

Where, L1 = Unknown self-inductance with internal resistance R1

R2 = Variable non-inductive resistance

R3 = Fixed standard non-inductive resistance

C2 = Standard variable capacitor

C4 = Fixed standard capacitor

Measurement of Capacitance

The capacitance can be measured with the help of the following bridges

De-Sauty Bridge

Where, C1 = Unknown capacitor

C2 = Standard capacitor

R3, R4 = Fixed non-inductive resistance

De-Sauty bridge can be used for the measurement of either air-cored or gas-filled capacitance only (loss less capacitor).

Schering Bridge

Dissipation factor D1 = tan δ = ωC1r1 = ωC4 R4

Where, C1 = Unknown capacitor with loss component r1

C2 = Fixed standard capacitor

R3 = Fixed standard non-inductive resistance

C4 = Variable capacitor

R4 = Variable non-inductive resistance

Key Points

• High voltage Schering bridge is used for the determination of capacitance of insulators, capacitor bushings and insulating oil and other insulating materials.
• The Schering bridge is also used to measure of relative permittivity of dielectric materials.
• The Schering Bridge is one of the most widely used AC bridges.
• In order to measure the low value of capacitance Schering bridge is used.

Measurement of Frequency

Frequency by Wein’s bridge.

Wein’s Bridge

Frequency, 

For R1 = R2 = R

and C1 = C2 = C

and C1 = C2 = C

• Wein’s bridge is used as a natch Fitlter in harmonic distortion analyzer.
• A frequency isolator in high-frequency oscillator and amplifier circuit.
• A notch filter in a harmonics distortion analyser where is used to isolate and eliminate the fundamental frequency component from the output of the amplifier under test.

Wagner’s Earthing Device

It is used to eliminate the effect of earth capacity-ance in the measurement of capacitors using the Schering bridge and it is also used for high accuracy in measurement.

Key Points

• Carey-foster bridge is specially designed to determine the difference between two nearly equal resistances.
• The potentiometer wire should have high specific resistance and low-temperature coefficient.
• The sensitivity of a potentiometer can be increased by increasing the length of the potentiometer wire.

Comparison between Different Types of Bridges

DC & AC Potentiometer

DC Potentiometer

This is a very basic instrument used for comparing emf two cells and for calibrating the ammeter, voltmeter and watt-meter. The basic working principle of the potentiometer is very very simple. Suppose we have connected two batteries head-to-head and tale-to-tale through a galvanometer. That means the positive terminals of both batteries are connected together and the negative terminals are also connected together through a galvanometer.

• Since a potentiometer measures voltage, it can also be used to detect current simply by measuring the voltage drop produced by the unknown current passing through a known standard resistance.
• The potentiometer is extensively used for the calibration of voltmeters and ammeters and has in fact become the standard for the calibration of these instruments. For the above-mentioned advantages, the potentiometer has become very important in the field of electrical measurements and calibration.

Standardization: Since the resistance of the slide wire is known accurately, the voltage drop along the slide wire can be controlled by adjusting the value of the working current. The process of adjusting the working current so as to match the voltage drop across a portion of sliding wire against a standard reference source is known as "Standardization".

Here in the figure, it is clear that 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 a potentiometer depends upon this phenomenon.

Now by adjusting the sliding contact on the resistor, it is found that the null deflection of the galvanometer comes for a first cell at a length of L on the scale and after positioning to way switch to the 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. Let's think of the first cell as a standard cell and its emf is E and the second cell is an unknown cell whose emf is E1. Now as per the above explanation,

E = Lv volt and
E1 = L1v volt
Dividing one equation by another, we get

As the emf of the standard cell is known, hence emf of the unknown cell can easily be determined.

A.C Potentiometer

The Potentiometer is an instrument which measures an unknown voltage by balancing it with a known voltage. The known source may be DC or AC. The working phenomenon of the DC potentiometer and AC potentiometer is the same. But there is one major difference between their measurements, the DC potentiometer only measures the magnitude of the unknown voltage. Whereas, the AC potentiometer measures both the magnitude and phase of unknown voltage by comparing it with known reference.

There are two types of AC potentiometers:

• Polar-type potentiometer.
• Coordinate type potentiometer.

Polar type Potentiometer

In such types of instruments, two separate scales are used to measure magnitude and phase angle on some reference of the unknown e.m.f. There is a provision on the scale that it could read phase angles up to 3600. It has an electrodynamometer-type ammeter along with a DC potentiometer and phase-shifting transformer which is operated by a single-phase supply.

• In a phase-shifting transformer, there is a combination of two ring-shaped laminated steel stators connected perpendicularly to each other, One is directly connected to the power supply and the other one is connected in series with variable resistance and capacitor.
• The function of the series components is to maintain a constant AC supply in the potentiometer by doing small adjustments in it. Between the stators, there is a laminated rotor having slots and winding which supplies voltage to the slide-wire circuit of the potentiometer.
• When current start flowing from stators, the rotating field is developed around the rotor and due to it e.m.f. is induced in the rotor winding.

The induced emf in the rotor winding by the stator winding 1 can be expressed as

E1 = KI sin wt .cosΦ

The induced emf in the rotor winding by the stator winding 2

E1 = KI (sinwt+90o).(cosΦ+90o)

From the above equation, we get Therefore, the resultant induced emf in the rotor winding due to two stator winding  Where Ø gives the phase angle.

Coordinate type Potentiometer

• In the coordinate AC potentiometer, two separate potentiometers are caged in one circuit.
• The first one is named the in-phase potentiometer which is used to measure the in-phase factor of an unknown e.m.f. and the other one is named as quadrature potentiometer which measures the quadrature part of the unknown e.m.f. the sliding contact AA’ in the in-phase potentiometer and BB’ in the quadrature potentiometer are used for obtaining the desired current in the circuit.
• By adjusting rheostat R and R’ and sliding contacts, the current in the quadrature potentiometer becomes equal to the current in the in-phase potentiometer and a variable galvanometer shows the null value.
• S1 and S2 are signs-changing switches which are used to change the polarity of the test voltage if it is required for balancing the potentiometer.
• There are two step-down transformers T1 and T2 which isolate the potentiometer from the line and give earthed screens protection between the winding.
• It also supplies 6 volts to potentiometers.

 Thus, the resultant voltage of the coordinate AC potentiometer is

And the phase angle is given by

Applications of AC Potentiometer

• Measurement of self-inductance.
• Calibration of voltmeter.
• Calibration of Ammeter.
• Calibration of wattmeter.

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