# Maxwell's Bridge - Circuit, Types, Equation, Phasor Diagram and Advantages

The Maxwell’s bridge or Maxwell’s Wein bridge is an AC bridge used to find or measure the unknown self-inductance. There are different types of ac bridges used for the measurement of self-inductance in which Maxwell’s bridge is the most commonly used bridge. The bridge uses the principle of null-deflection i.e., by balancing the impedances on the bridge arms. The equation obtained when the bridge is balanced (i.e., ratio of impedances are balanced) can be used to determine the unknown inductance connected to it.

## Maxwell’s Inductance Bridge :

In Maxwell's inductance bridge the unknown self-inductance to be measured is compared with the known inductance. Hence the unknown self-inductance and internal resistor of an inductor can be measured with Maxwell's inductance bridge. The circuit diagram is shown in the below figure.

### Phasor Diagram of Maxwell’s Inductance Bridge :

In Maxwell's inductance bridge, the resistance R2 is the decade resistance box. The resistor R3 and R4 can have their values as from 10, 100, 1000, and 10,000 Ω by the successive adjustment of L2 and R2. The balance of the bridge can be adjusted. The phasor diagram of Maxwell's inductance bridge under balance condition is shown below.

## Maxwell’s Inductance Capacitance Bridge :

Maxwell’s inductance capacitance bridge is also similar to Maxwell’s inductance bridge seen above. But here the unknown self-inductance to be determined is compared with the standard known capacitor. The circuit diagram for Maxwell’s inductance capacitance bridge is shown in the below figure.

#### The advantages of using a standard capacitor in Maxwell's bridge are as follows,The standard capacitors used in Maxwell's bridge are of low cost compared to the stable and accurate standard inductors.These capacitors are small in size.The capacitors used in this bridge are lossless capacitors as there is less possibility of losing energy.The capacitor is independent of the external fields. Whereas, the stray magnetic fields can be eliminated by providing proper shielding on the standard inductor.In Maxwell's inductance bridge, there is a requirement of adjusting the current flow through the inductor to show the rated value of inductance.Let,L1 = Unknown inductance to be measuredR1 = Resistance of the unknown inductorR2, R3 = Standard non-inductive resistancesR4 = Standard non-inductive variable resistanceC4 = Standard variable capacitor. From the above figure, the impedances of the respective arms are given as, Under balanced condition (i.e., when detector shows null deflection), we have, Equating the real and imaginary terms on both sides, we get, Thus, the bridge can be balanced by varying R4 and C4. The Q-factor or storage factor of the inductor is given by,

From the above expression for Q factor obtained from Maxwell's inductance capacitance bridge. The value of the Q factor is proportional to the product of R4 and C4. We know that, usually, the value of C4 will be in μF or pF.

In order to have a greater value of Q factor, R4 must be in megaohms or greater than that, so that the product is high. Resistance of such a high value is very difficult to obtain and also very costly. Hence, the measurement of inductance using Maxwell's inductance-capacitance bridge is limited to low range values of Q i.e., between 1 and 10. Hay's bridge is used for high Q factor coils.

The below shows the phasor diagram for Maxwell's inductance capacitance bridge.

Also, from the equations of L1, it is clear that L1 is the product of R2, R3, and C4. The value of C4 is usually in μF. Now if the value of R2 and R3 is selected such that R2 R3 is 106 then L1 = 106 × C4 × 10-6 = C4. Hence, the dial of the variable capacitor C4 will directly give the value of inductance.