**Measurement Of Self Inductance By Maxwell’s Inductance Bridge:**

**Maxwell’s inductance Bridge** circuit measures an inductance by comparison with a variable standard self-inductance.The connections and the phasor diagrams for balance conditions are shown in the **Maxwell’s Inductance Bridge** figure.

#### Let

#### L1 = unknown inductance of resistance R1

#### L2 = variable inductance of fixed resistance r2

#### R2 = variable resistance connected in series with inductor L2

#### R3,R4 = known non-inductive resistances

#### The theory of **Maxwell’s Inductance Bridge** has been explained already in ac bridges post.

#### Resistors R3 and R4 are normally a selection of values from 10, 100, 1000 and 10,000 r2 is a decade resistance box.In some cases, an additional known resistance may have to be inserted in series with the unknown coil in order to obtain balance.

**Measurement Of Self Inductance By Maxwell’s Inductance Capacitance Bridge: **

#### In *Maxwell’s Inductance Capacitance Bridge*, an inductance is measured by comparison. with a standard variable capacitance. The connections and the phasor diagram at the balance conditions are given in **Maxwell’s Inductance Capacitance Bridg**e figure below.

Let L1 = unknown inductance,

R1 = effective resistance of inductor L1,

R2, R3, R4 = known non-inductive resistances,

and C4 = variable standard capacitor.

Thus we have two variables R4 and C4 which appear in one of the two balance equations and hence the two equations are independent.

####

The expression for Q factor,

Q = ωL₁/R₁ = ωC₄R₄

**Advantages of Maxwell’s Inductance Capacitance Bridge:**

#### The advantages of **Maxwell’s Inductance Capacitance Bridge** are

1.The two balance equations are independent if we choose R4 and C 4 as variable elements.

2.The frequency does not appear in any of the two equations.

3.**Maxwell’s Inductance Capacitance Bridg**e yields a simple expression for unknowns L1 and R1 in terms of known bridge elements.

Physically R2 and R3 are each, say, 10, 100,1000 or 10,000 Q and their value is selected to give suitable value of product R2R3 which appears in both the balance equations; C4 is decade capacitor and R4 a decade resistor.

The simplicity of the bridge can be appreciated by the following example. Suppose the product R2R3 is 10⁶.Therefore, inductance is L1= C4 x 10⁶. Thus when the balance is achieved the value of C4 in μF directly gives the value of inductance in H.

4.The **Maxwell’s inductance capacitance bridge** is very useful for measurement of a wide range of inductance at the power and audio frequencies.

**Disadvantages of Maxwell’s Inductance Capacitance Bridge: **

#### The main disadvantages of **Maxwell’s inductance capacitance bridge** are

1.**Maxwell’s Inductance Capacitance Bridge** requires a variable standard capacitor which may be very expensive if calibrated to a high degree of accuracy.Therefore sometimes a fixed standard capacitor is used, either because a variable capacitor is not available or because fixed capacitors have a higher degree of accuracy and are less expensive than the variable ones. The balance adjustments are then done by

(a) either varying R2 and R4 and since R2 appears in both the balance equations, the balance adjustments become difficult

(b) putting an additional resistance in series with the inductance under measurement and then varying this resistance and R4.

2.The bridge is limited to measurement of low Q coils, (1 < Q < 10). It is clear that the measurement of high Q coils demands a large value for resistance R4, perhaps 10⁵ or 10⁶. The resistance boxes of such high values are very expensive. Thus for values of Q > 10, **Maxwell’s bridge** is unsuitable.

####

The *Maxwell’s bridge* is also unsuited for coils with a very low value of Q (i.e., Q < 1). Q values of this magnitude occur in inductive resistors, or in an R.F. coil if measured at low frequencies. The difficulty in measurement occurs on account of labour involved in obtaining balance since nominally a fixed capacitor is used and balance is obtained by manipulating resistances R2 and R4 alternately.This difficulty is explained as below:

#### A preliminary inductive balance is made with R2 and then R4 is varied to give a resistive balance which is dependent on the R2 setting.Accordingly, when R2 is changed for a second inductive balance, the resistive balance is disturbed and moves to a new value giving slow “convergence” to balance.This is particularly true of a low Q coil, for which resistance is prominent (as = wL/ R).

Thus a sliding balance condition prevails and it takes many manipulations to achieve balance for low Q coils with *Maxwell’s bridge*.From the above discussions, we conclude that **Maxwell’s bridg**e is suited for measurements of only medium Q coils.