The document Chapter 1 (Part 1) AC Bridges - Notes, Electrical Measurement, Electrical Engineering | EduRev Notes is a part of the Electrical Engineering (EE) Course Electrical Engineering SSC JE (Technical).

All you need of Electrical Engineering (EE) at this link: Electrical Engineering (EE)

**A.C. BRIDGES**** Introduction: **The

These bridge methods are very useful for the measurement of:

- Inductance (L)
- Capacitance (C)
- Frequency (f)
- Mutual inductance (M)
- Storage factor
- Loss factor, etc.

__Types of Sources in AC Bridges__

- For Low frequency measurement the power line supply can serve as the source of excitation.
- For High frequency measurement the electronic oscillator is used as excitation voltage.

__Types of detectors in AC Bridges__**Head phones:**

- It is used at frequencies of 250 Hz and over upto 3 to 4 KHz.
- Most sensitive detector for this ranges of frequency.

**Vibration galvanometer**

- It can be used from 5 Hz to 1000 Hz but suitable mainly upto 200 Hz.
- They are extremely useful for power and low AF ranges.

**Tuneable Amplifier Detector (TAD)**

- It can be used at 10 Hz to 100 KHz.

**Cathode Ray Oscilloscope (CRO)**

- It is used for higher frequency more than 5 KHz.

**Note: **For a **DC Bridge **, the **“PMMC ” **instrument acts as a detector.

__AC bridges through which inductance (L) is measured:__

1. Maxwell’s inductance bridge.

2. Maxwell’s inductance-capacitance bridge.

3. Hay’s bridge.

4. Anderson’s bridge.

5. Owen’s bridge.

**1. Maxwell’s Inductance Bridge: **This bridge measures an unknown inductance by comparison with a variable standard self inductance.

Let R_{1} and L_{1} are unknown quantity

L_{2} = Variable inductance of fixed resistance ‘r_{2}’

R_{2} = Variable resistance connected in series with “L_{2}”

R_{3} and R_{4} = Known non-inductive resistances.

At balance condition,

equation real and imaginary part we get,

and

**2. Maxwell’s Inductance-capacitance Bridge: **This Bridge measures an unknown inductance in terms of a known capacitance.

Let R_{1} and L_{1 }are unknown quantity R_{2}, R_{3} and R_{4 }are known non-inductive resistances and C_{4} = variable standard capacitor

At balance condition, Z_{1}Z_{4} = Z_{2}Z_{3}

Equating real part we get,

and equating imaginary part we get,

**Quality factor:**

**Advantages:**

• Circuit is simple.

• Obtained balance equations are free from the frequency term.

• Balance equations are independent if we choose R_{4} and C_{4} as variable elements.

• It is very useful for measurement of a wise range of inductances at power and audio frequencies.

**Disadvantages:**

• It requires variable standard capacitor which is very costly.

• The bridge is limited to measurement of low quality coils (1 < Q < 10) and it is also unsuitable for low value of Q (i.e. Q < 1) from this we conclude that a Maxwell bridge is used suitable only for medium Q coils.**3. HAY’s Bridge:****• **It is a modification of Maxwell’s bridge.

• This bridge uses a resistances in series with the standard capacitor as shown in figure below,

Let,R_{1} and L_{1} are unknown quantity

R_{2}, R_{3} and R_{4} are non-inductive resistances.

and C_{4} = standard capacitor

At balance condition,

Z_{1}Z_{4 }= Z_{2}Z_{3}

Equating real and imaginary parts we get,

and

**Quality factor** =

i.e.

Now

and

• In this bridge, the expression for the unknown inductance and resistance involves the frequency term.

So, for the higher Q (i.e. Q > 10) 1 + (1/Q)^{2} ≈ 1 and then,

• So, we can say this bridge is suitable for high Q-coils (i.e. Q > 10)

**Advantages:****• **It gives a simple expression for Q-factor.

• For high Q-coils it gives simple expression for unknown R_{1} and L_{1}.

**Disadvantages:****• **It is not suitable for medium or low Q-coils.

** **

**4. ANDERSON’s Bridge:****• **It is a modification of the Maxwell ’s inductance-capacitance bridge.

• In this bridge method, the self inductance is measured in terms of standard capacitor

At balanced condition, V_{b} = V_{e}

So, I_{D} = 0

Also for the Delta network

we can convert this in star form

as

So,

For balance condition, Z_{ab}.Z_{c} = Z_{a}N.Z_{bc}

Equating real part we get,

Now equating imaginary part we get,

L_{1} R_{4} = R_{3}C[R_{2} R_{4} + rR_{2} + rR_{4}]

**Phasor diagram for Anderson’s bridge n/w:**

**Quality factor =**

• For Low Q-coil, L_{1} and C So, it is suitable for Low Q-coils (i.e. Q < 1).**Advantages:**

• It may be used for accurate estimation of capacitance in terms of inductance.

• It is relatively cheaper because here fixed capacitance is used.

• It is much easier to obtain the balance.

**Disadvantage:**

• It is more complex circuit.

• The balance equations are not simple and in fact are much more tedious.

• An additional junction point increases the difficulty of shielding the bridge network.

**5. OWEN’s Bridge:****• **This bridge may also be used for the measurement of inductance in terms of capacitance.

Let R_{1} and L_{1} are the unknown quantity

R_{2} = Variable non-inductive resistance

R_{3} = Fixed non-inductive resistance

C_{2} = Variable standard capacitor

C_{4 }= Fixed standard capacitor

At balance condition,

Z_{ab}Z_{cd} = Z_{ad} . Z_{bc}

Equating real and imaginary part we get,

and

L_{1} = R_{2} R_{3} C_{4}**Quality factor **= **Advantages:****• **It has independent balance equations.

• The unknown quantities expressions are free from frequency term.

This can be used over a wide range of measurement of inductances.

**Disadvantages:**

• It requires a variable capacitor so it is very costly network.

• Its accuracy is about only 1%.

__AC bridges through which capacitances are measured__

1. De Sauty’s bridge

2. Schering bridge**1. De Sauty’s Bridge:**

• It is the simplest method of comparing two capacitances.

• It may also be used for determining the dissipation factor (D).**Note:**

then D = tan δ = ωC_{s} r_{s}

then D = tan

δ = 1/ωC_{p} r_{p}

Considering ideal capacitors, the bridge circuit is,

Let C_{1 }= unknown capacitor

C_{2} = a standard capacitor

R_{3} and R_{4} = non-inductive resistors

At balance condition:

Z_{ab} . Z_{cd} = Z_{ad} . Z_{bc}

The advantage of this bridge is its simplicity but from this we can not determine “Dissipation Factor (D)”, so some modification are needed in the above bridge.

Now we consider the lossy capacitor and bridge in becomes **“Modified De-Sauty’s Bridge”.**

• Given C_{2} so, D_{2} = ωC_{2}r_{2} and we have to estimate C_{1} and hence D_{1} = ωC_{1}r_{1 }

At balance condition,

Z_{ab} . Z_{cd }= Z_{bc} . Z_{ad}

Equating real part we get, (R_{1} + r_{1})R_{4 }= (R_{2} + r_{2})R_{3}

Now equating imaginary part we have,

and

Also,

• This bridge can not determine the accurate result for dissipation factor because we have,

D _{2} – D_{1} = ω[C_{2}r_{2} – C_{1}r_{1}]

Since (D_{2} – D_{1}) is very-very small so its is difficult to determine “D_{1}” accurately.

**2. Schering Bridge**

The Schering bridge use for measuring the capacitance of the capacitor, dissipation factor, properties of an insulator, capacitor bushing, insulating oil and other insulating materials. It is one of the most commonly used AC bridge. The Schering bridge works on the principle of balancing the load on its arm.

**In this diagram:**** **

- C
_{1}= capacitor whose capacitance is to be determined - R
_{1}= a series resistance representing the loss in the capacitor C_{1} - C
_{2}= a standard capacitor - R
_{3}= a variable non-inductive resistance - C
_{4 }= a variable capacitor - R
_{4}= a non-inductive resistance in parallel with the variable capacitor C_{4}

When the bridge is in the balanced condition, zero current passes through the detector, which shows that the potential across the detector is zero. At balance condition

Z_{1}/Z_{2} = Z_{3}/Z_{4}

Z_{1}Z_{4} = Z_{2}Z_{3}

Substituting the values of z_{1}, z_{2}, z_{3} and z_{4} in the above equation, we get

Equating the real and imaginary parts and the separating we get,

Let us consider the phasor diagram of the above Schering bridge circuit and mark the voltage drops across ab,bc,cd and ad as e_{1}, e_{3},e_{4} and e_{2} respectively. From the above Schering bridge phasor diagram, we can calculate the value of tanδ which is also called the dissipation factor.

The equation that we have derived above is quite simple and the dissipation factor can be calculated easily.

**Advantages of Schering Bridge:**

1. Balance equations are free from frequency.

2. The arrangement of the bridge is less costly as compared to the other bridges.

78 docs|37 tests

### Chapter 2 Cathode Ray Oscilloscope - Notes, Electrical Measurement, Electrical Engineering

- Doc | 3 pages
### Chapter 3 Electromechanical Indicating Type Instruments(Part - 1) - Notes, Electrical Measurement

- Doc | 6 pages
### Chapter 3, Electromechanical Indicating Type Instruments (Part - 2) - Notes, Electrical Measurement

- Doc | 8 pages