Measurement of Self Inductance , Maxwell's Bridge

Maxwell's Inductance Bridge: The bridge circuit measures unknown inductance by comparison with a variable standard self-inductance.

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.

By solving balance equations of the bridge we get

                          L1=(R3/R4).L2

                          R1=(R3/R4)(R2+r2)

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

Maxwell's Inductance-Capacitance Bridge:

In this bridge, inductance is measured by comparison with a variable standard capacitance.

Let L1=unknown inductance,   R1= effective resistance of inductor L1,

      R2, R3, R4=known non-inductive resistances, and C4=variable standard capacitor.

 

Writing an equation for balance

(R1+jwL1)(R4/(1+jwC4R4))=R2.R3

Separating the real and imaginary parts and solving we get:

                                R1=(R2.R3)/R4

                        and  L1=R2.R3.C4

  the two variables R4 and C4 appear in different equations so the equations are independent.

The expression for Q factor Q= (w.L1)/R1 = w.C4.R4

Advantages 

• The two balance equations are independent if we choose R4 and C4 as variable elements.
• The frequency does not appear in any of the two equations.
• This equation gives a simple expression for unknowns L1 and R1 in terms of bridge elements.
• for example, if we consider R2.R3=10^6 then 
•                                L1=C4.10^6
• thus if balance is achieved then if the value of capacitance is in micrometer then it gives the direct value of inductance in henry.
• Maxwell's inductance-capacitance bridge is very useful for the measurement of a wide range of inductance at power and audio frequencies.

Disadvantages

1.    The variable capacitor is very expensive if calibrated to a high degree of accuracy

Therefore sometimes a fixed capacitor is used which is known for a high degree of accuracy. In this case, balance is obtained by

(a)   either varying R2 and R4 since R2 appears in both equations thus balance adjustment becomes difficult.

(b) putting additional series resistance with inductance and varying this and R4.

2.    The bridge is limited to measurement of low Q (1<Q<10) .Because for high Q value of R4 must be high as 10^5 or 10^6 and the resistance box with such high resistance is very expensive. Thus bridge is unsuitable for Q>10.

The bridge is also unsuitable for low Q (Q<1) . Because for low Q obtaining balance condition is difficult due to the sliding effect.

 ( The capacitance is generally fixed in the measurement of balance point thus we change values of R2 and R4 and this comes in both equations so if we change one then another variable changes and balance disturbs so we need to do many manipulations) 

Thus we see from the above discussion Maxwell's bridge is suitable for the measurement of medium Q values only.

Reference:

-Swerny