## What is Maxwells Bridge : Circuit, Phasor Diagram & Applications

- Frank
- May 25, 2022
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The circuits which are used to calculate the unknown resistance, inductance, capacitance, frequency and mutual inductance are called AC bridges. These circuits operate with an AC voltage signal. These bridges work on the principle of balance ratio of impedances which is obtained by the null detector and produces accurate results. In some of the circuits, an AC amplifier can be used instead of the null detector. The balance equations obtained from the circuit can be used to determine the unknown resistance, capacitance, and inductance and also independent of frequency. The AC bridges are used in communication systems, complex electrical and electronic circuits and many more. There are different types of AC bridges used in electronic circuits. They are Maxwells bridge, Maxwells Wein bridge, Anderson bridge, Hay’s bridge, Owen bridge, De Sauty bridge, Schering bridge, and Wein series bridge.

### Maxwells Bridge Definition

Maxwell’s bridge is also known as Maxwell’s Wein bridge or modified form of Wheatstone bridge or Maxwell’s inductance capacitance bridge, consists of four arms used to measure unknown inductances in terms of calibrated capacitances and resistances. It can be used to measure unknown inductance value and compares it with the standard value. It works on the principle of comparison of known and unknown inductance values.

It uses the null deflection method to calculate inductance with a parallel calibrated resistor and capacitor. The Maxwell’s bridge circuit is said to be in resonance if the positive phase angle of an inductive impedance is compensated with the negative phase angle of the capacitive impedance (connected in the opposite arm). Hence there will be no current flowing through the circuit and no potential across the null detector.

### Maxwells Bridge Formula

If the maxwell’s bridge is in balance condition, the unknown inductance can be measured by using a variable standard capacitor. The maxwell’s bridge formula is given as (in terms of inductance, resistance, and capacitance)

**R1 = R2r3/R4**

**L1= R2R3C4**

The quality factor of Maxwell’s bridge circuit is given as,

**Q = ωL1/R1 = ωC4R4**

### Maxwells Bridge Circuit

Maxwell’s bridge circuit consists of 4 arms connected in square or rhombus shape. In this circuit, two arms contain a single resistor, another one arm contains a resistor and inductor in series combination, and the last arm contains a resistor and capacitor in parallel combination. The basic Maxwell’s bridge circuit is shown below.

An AC voltage source and a null detector are connected in diagonal to the bridge circuit to measure the unknown inductance value and compared with the known values.

### Maxwells Bridge Equation

From the circuit, AB, BC, CD, and DA are the 4 arms connected in rhombus shape.

AB and CD are the resistors R2 and R3,

BC is a series combination of resistor and inductor given as Rx and Lx.

DA is a parallel combination of resistor and capacitor given as R1 and C1

Consider Z1, Z2, Z3, and ZX are the impedances of the 4 arms of the bridge circuit. The values for these impedances are given as,

**Z1 = (R1+jwL1) [ since Z1=R1+1/jwC1 ]**

**Z2 = R2**

**Z3=R3**

**ZX= (R4+jwLX)**

Or

**Z1= R1 in parallel with C1 that is, Y1=1/Z1**

**Y1 = 1/R1 + j ωC1**

**Z2=R2**

**Z3=R3**

**Zx=Rx in series with Lx =Rx+jωLx**

Take the balance equation of a basic AC bridge circuit as follows,

**Z1Zx=Z2Z3**

**Zx=Z2Z3/Z1**

Substitute the values of impedances of Maxwell’s bridge circuit in the above balance equation. Then,

**Rx+jωLx = R2R3 ((1/R1)+jωC1)**

**Rx+jωLx = R2R3/R1+ jωC1R2R3**

Now equate the real and imaginary terms from the above two equations,

**Rx = R2R3/R1 and Lx =C1R2R3**

**Q = ωLx/Rx = ωC1R2R3x R1/R2R3 = ωC1R**

Where Q = quality factor of the bridge circuit

Rx= unknown resistance

Lx= unknown inductance

R2 and R3 = known non-inductive resistances

C1 = capacitor connected in parallel to the variable resistor R1

### Phasor Diagram

Maxwell’s bridge is used to measure the unknown inductance of the circuit by using calibrated resistors and capacitors. This bridge circuit compares the known inductance value with a standard value. **Maxwell’s bridge phasor diagram** circuit in the balance condition is shown below.

The Maxwell’s bridge circuit is said to be in a balanced condition if the phase shifts of inductors and capacitors are opposite to each other. That means Capacitive impedance and inductive impedance are placed opposite to each other in the bridge circuit. The current I3 and I4 are in phase with I1 and I2. By varying the impedances of the bridge circuit, the current may lag behind the applied AC voltage signal.

Measurement errors can be eliminated due to the mutual inductance between the two indicators. Since substantial errors can be occurred due to the coupling between the coils in the circuit. To achieve the balance condition of the circuit, the variable capacitor and resistor are connected in parallel. The measured inductances in a balance condition are independent of frequencies.

### Types of Maxwells Bridge

The different types of bridges are

### Maxwells Inductance Bridge

This type of bridge circuit is used to measure the unknown inductance value of the circuit by comparing it with a standard value of self-inductance. Two arms of the bridge circuit known non-inductive resistances, another one arm contains variable inductance with a fixed resistor in series, and another one arm contains unknown inductance in series with a resistor. The AC voltage source and a null detector are connected across the junctions of the circuit. The circuit diagram is shown below.

At the balance condition, the formula for Maxwell’s inductance circuit is given as,

Where L1= Unknown inductance with a resistor R1

R2 and R3 are the non-inductive resistances

L2 is the variable inductance with a fixed Resistance r2

R2 is the variable resistor in series with L2

### Maxwells Inductance Capacitance Bridge

This type of bridge circuit is used to measure unknown inductance value by comparing it with a variable standard capacitor. The AC voltage signal and a null detector are connected at the junctions.

From the circuit, we can observe that,

One arm contains variable standard capacitor C1 in parallel with a variable non-inductive resistance R1

The other two arms contain known non-inductive resistors R2 and R3

Another arm contains unknown inductance Lx with a resistor Rx in series whose value to be measured and compared with a known value.

The expression for Maxwell’s inductance capacitance is given as, ( in balance condition

Q = quality factor of Maxwell’s bridge circuit

### Advantages of Maxwells Bridges

The advantages are

- At the balance condition, the bridge circuit is independent of frequency
- It helps to measure a wide range of inductance values at audio and power frequency
- To measure the inductance value directly, the scale of calibrated resistance is used.
- It is used to measure the high range of inductances and compared with a standard value.

### Disadvantages of Maxwells Bridge

The disadvantages are

- The fixed capacitor in Maxwell’s bridge circuit may create interaction between resistance and reactance balance.
- It is not suitable to measure a high range of quality factor ( Q values >=10)
- The variable standard capacitor used in the circuit is very costly.
- It is not used to measure the low-quality factor ( Q value) due to the circuit balance condition. Hence it is used for medium quality coils.

### Applications of Maxwells Bridge

The applications are

- Used in communication systems
- Used in electronic circuits
- Used in power and audio frequency circuits
- Used to measure unknown inductance values of the circuit and compared with a standard value.
- Used to measure medium quality coils.
- Used in filter circuits, instrumentation, linear and non-linear circuits
- Used in power conversion circuits.

### FAQs

**1). What are AC and DC bridges?**

The AC bridges and DC bridges are used to measure unknown components like inductance, capacitance, and resistance. Or measure unknown impedances of the circuit.

The different types of ac bridges are Maxwell’s bridge, Maxwell’s Wien bridge, Anderson bridge, Hay’s bridge, Owen bridge, De Sauty bridge, Schering bridge, and Wein series bridge.

The DC bridges are used to measure unknown resistance in the bridge circuit. The different types of DC bridges are Wheatstone’s bridge, Kelvin bridge, and strain gauge bridge.

**2). Which bridge is frequency sensitive?**

Wien’s bridge is frequency sensitive.

**3). What is the purpose of a bridge circuit?**

The purpose of the bridge circuit is to rectify the electric current in the power supply and measure the unknown impedance of the circuit and compared it with a known value.

**4). What is the formula of self-inductance?**

When the flux is known, the formula for self-inductance is given as,

L = NΦm/I.

Where ‘L’ is the self – inductance in Henry’s

‘Φm’ is the magnetic flux in the coil

‘N’ is the number of turns

‘I’ is the current flowing through the coil in Amperes.

**5). What are RC and LC oscillators?**

LC oscillator uses the inductor-capacitor tank circuit and it is a type of positive feedback oscillator to produce sustained oscillations.

The linear oscillator which uses resistors and capacitors to form the RC network with positive feedback is called the RC oscillator. It is also known as a sinusoidal oscillator.

Thus this is all an overview of Maxwell’s bridge circuit’s definition, types, formula, equation, types, applications, advantages, and disadvantages. Here is a question for you, “what are the other types of bridge circuits?”