A.C Bridges & Potentiometer | GATE Notes & Videos for Electrical Engineering - Electrical Engineering (EE) PDF Download

AC Bridges


AC bridges are used to measure self inductance, mutual inductance, capacitance and frequency.

Types of Sources
  1. At low frequency, power line is used as source.
  2. At high frequency, electronic oscillator are used as source
Types of Detectors
  1. Vibration galvanometer at low power frequency and audio frequency (upto 1000 Hz)
  2. Head phones at audio frequency (250 Hz to 4 kHz)
  3. Tuneable amplifier for frequency range (10 Hz to 100 kHz)

General Bridge Circuit
At balanced bridge A.C Bridges & Potentiometer | GATE Notes & Videos for Electrical Engineering - Electrical Engineering (EE)
Magnitude condition | Z1 || Z4 | = | Z2 || Z3 |
Angle condition ∠θ1 + θ4 = ∠θ2 + ∠θ2 

General bridge circuitGeneral bridge circuit

For balanced bridge both the magnitude

Measurement of Self Inductance

  1. Maxwell’s inductance bridge
  2. Maxwell’s inductance-capacitance bridge
  3. Hay’s bridge
  4. Anderson’s bridge
  5. Owne’s bridge

1. Maxwell’s Inductance Bridge

A.C Bridges & Potentiometer | GATE Notes & Videos for Electrical Engineering - Electrical Engineering (EE)

A.C Bridges & Potentiometer | GATE Notes & Videos for Electrical Engineering - Electrical Engineering (EE)
Where, L1 = Unknown inductance of resistance R1
L2 = Variable inductance
R2 = Standard variable resistance
R3, R4 = Fixed non-inductance resistance

2. Maxwell’s Inductance - Capacitance Bridge
A.C Bridges & Potentiometer | GATE Notes & Videos for Electrical Engineering - Electrical Engineering (EE)

A.C Bridges & Potentiometer | GATE Notes & Videos for Electrical Engineering - Electrical Engineering (EE)

Q-factor,
A.C Bridges & Potentiometer | GATE Notes & Videos for Electrical Engineering - Electrical Engineering (EE)
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 balanced bridge obtained as

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

3. Hay’s Bridge

A.C Bridges & Potentiometer | GATE Notes & Videos for Electrical Engineering - Electrical Engineering (EE)

A.C Bridges & Potentiometer | GATE Notes & Videos for Electrical Engineering - Electrical Engineering (EE)
Where, C4 = Standar capacitance
Q-factor
A.C Bridges & Potentiometer | GATE Notes & Videos for Electrical Engineering - Electrical Engineering (EE)
for Q > 10 i.e., high Q-coils
L1 = R2R3C

4. Anderson’s Bridge

A.C Bridges & Potentiometer | GATE Notes & Videos for Electrical Engineering - Electrical Engineering (EE)
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

A.C Bridges & Potentiometer | GATE Notes & Videos for Electrical Engineering - Electrical Engineering (EE)

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

Key Points

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

5. Owen’s Bridge

A.C Bridges & Potentiometer | GATE Notes & Videos for Electrical Engineering - Electrical Engineering (EE)

A.C Bridges & Potentiometer | GATE Notes & Videos for Electrical Engineering - Electrical Engineering (EE)
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 following bridges

  1. De-Sauty Bridge
    A.C Bridges & Potentiometer | GATE Notes & Videos for Electrical Engineering - Electrical Engineering (EE)A.C Bridges & Potentiometer | GATE Notes & Videos for Electrical Engineering - Electrical Engineering (EE)
    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).
  2. Schering Bridge
    A.C Bridges & Potentiometer | GATE Notes & Videos for Electrical Engineering - Electrical Engineering (EE)A.C Bridges & Potentiometer | GATE Notes & Videos for Electrical Engineering - Electrical Engineering (EE)
    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 determination of capacitance of insultaors, capacitor bushings and insulating oil and other insulating materials.
  • Schering bridge is also used to measurement of relative permittivity of dielectric materials.
  • The Schering bridge is one of the most widely used AC bridges.
  • In order to measure low value of capacitance Schering bridge is used.

Measurement of Frequency


Frequency by Wein’s bridge.

  1. Wein’s Bridge
    A.C Bridges & Potentiometer | GATE Notes & Videos for Electrical Engineering - Electrical Engineering (EE)
    Frequency, 
    A.C Bridges & Potentiometer | GATE Notes & Videos for Electrical Engineering - Electrical Engineering (EE)
    For R1 = R2 = R
    and C1 = C2 = C
    A.C Bridges & Potentiometer | GATE Notes & Videos for Electrical Engineering - Electrical Engineering (EE)
    and C1 = C2 = C
    A.C Bridges & Potentiometer | GATE Notes & Videos for Electrical Engineering - Electrical Engineering (EE)
    • Wein’s bridge used as a natch Fitlter in harmonic distaration amalyzer.
    • A frequency isolator in high frequency oscillator and amplifier circuit.
    • A notch filter in a harmonics distortion analyser where it is used to isolate and elilminate 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 measurement of capacitor using Schering bridge and it also used for high accuracy in measurement.

  1. 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.
    • Sensitivity of a potentiometer can be increased by increasing the length of potentiometer wire.
  2. Comparison between Different Types of Bridges
    A.C Bridges & Potentiometer | GATE Notes & Videos for Electrical Engineering - Electrical Engineering (EE)

DC & AC Potentiometer

  1. DC Potentiometer
    This is a very basic instrument used for comparing emf two cells and for calibrating ammeter, voltmeter and watt-meter. The basic working principle of potentiometer is very very simple. Suppose we have connected two battery in head to head and tale to tale through a galvanometer. That means the positive terminals of both battery are connected together and 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 a 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 slide wire is known accurately, the voltage drop along the slide wire can be controlled by adjusting the value of 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".
      A.C Bridges & Potentiometer | GATE Notes & Videos for Electrical Engineering - Electrical Engineering (EE)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 potentiometer depends upon this phenomenon.
      A.C Bridges & Potentiometer | GATE Notes & Videos for Electrical Engineering - Electrical Engineering (EE)Now 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.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. Now as per above explanation,
      E = Lv volt and
      E1 = L1v volt
      Dividing one equation by other, we get
      E/E1 = L/L1
      As the emf of the standard cell is known, hence emf of the unknown cell can easily be determined.
  2. A.C Potentiometer
    The Potentiometer is an instrument which measures unknown voltage by balancing it with a known voltage. The known source may be DC or AC. The working phenomenon of DC potentiometer and AC potentiometer is same. But there is one major difference between their measurements, DC potentiometer only measures the magnitude of the unknown voltage. Where as, 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.

1. Polar type Potentiometer
In such type 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 angle up to 3600. It has electrodynamometer type ammeter along with DC potentiometer and phase-shifting transformer which is operated by single phase supply.

  • In phase-shifting transformer, there is a combination of two ring-shaped laminated steel stators connected perpendicularly to each other, One is directly connected to power supply and the other one is connected in series with variable resistance and capacitor.
  • The function of the series components is to maintain constant AC supply in the potentiometer by doing small adjustments in it. Between the stators, there is 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.A.C Bridges & Potentiometer | GATE Notes & Videos for Electrical Engineering - Electrical Engineering (EE)The induced emf in rotor winding by stator winding 1 can be expressed as
    E1 = KI sinwt.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
    E = KI (sinwt cos∅ - coswt sin∅)
    Therefore, resultant induced emf in the rotor winding due to two stator winding
    E = kI sin(wt - ∅)
    Where, Ø gives the phase angle.
2. Coordinate type Potentiometer
  • In coordinate AC potentiometer, two separate potentiometers are caged in one circuit.
  • The first one is named as 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 quadrature part of the unknown e.m.f. the sliding contact AA’ in the in-phase potentiometer and BB’ in 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 potentiometer from the line and give an earthed screens protection between the winding.
  • It also supplies 6 volts to potentiometers.
    A.C Bridges & Potentiometer | GATE Notes & Videos for Electrical Engineering - Electrical Engineering (EE)

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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FAQs on A.C Bridges & Potentiometer - GATE Notes & Videos for Electrical Engineering - Electrical Engineering (EE)

1. What is an AC bridge?
Ans. An AC bridge is a circuit commonly used in electrical engineering to measure unknown values of resistance, inductance, and capacitance. It consists of four arms, including a known component, and is balanced when the ratio of the unknown to the known component is determined.
2. How does an AC bridge work?
Ans. An AC bridge works on the principle of balance. By adjusting the known component or varying the frequency of the input AC signal, the bridge is balanced when the voltage across the null detector becomes zero. This balance condition helps determine the unknown value of the component in the bridge.
3. What is the difference between AC and DC potentiometer?
Ans. AC potentiometer is used to measure the unknown magnitude and phase angle of an AC source, while DC potentiometer is used to measure the unknown voltage or current of a DC source. The AC potentiometer uses a phase-sensitive detector, whereas the DC potentiometer uses a null detection principle.
4. How does a potentiometer work?
Ans. A potentiometer is a variable resistor with three terminals. It consists of a resistive element and a sliding contact, which can be moved along the resistive track. When a voltage is applied across the end terminals, the sliding contact can be adjusted to select a desired output voltage, making it useful for measuring unknown quantities.
5. What are the advantages of using AC bridges and potentiometers?
Ans. AC bridges and potentiometers provide accurate measurements of unknown electrical quantities, such as resistance, inductance, capacitance, voltage, and current. They offer high precision, good repeatability, and are versatile instruments for both laboratory and industrial applications. Additionally, they are relatively simple to use and provide a wide range of measurements.
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