Mumbai University > Electronics Engineering > Sem3 > Electronic Instruments and Measurements

Marks: 10M

Year: Dec 2014

In Maxwell’s inductance capacitance bridge, the value of inductance is measured by comparison with standard variable capacitance. The connection for Maxwell’s inductance capacitance bridge is shown in figure below.

Let

$L_1$=unknown inductance,

$R_1$=effective resistance of inductor $L_1$,

$R_2 R_3 R_4$=known non-inductive resistances,

$C_4$=variable standard capacitor.

And writing the equation for balance

$$(R_1+jwL_1)\Big(\frac{R_4}{1+jwC_4R_4}\Big)=R_2R_3 \\ R_1R_4+jwL_1R_4=R_2R_3+jwR_2R_3C_4R_4 $$

Separating the real and imaginary terms, we have

$$R_1=\frac{R_2R_3}{R_4}$$

And

$$L_1=R_2R_3C_4$$

Thus we have two variables $R_4$ and $C_4$ which appear in one of the two balance equations and hence the two equations are independent. The expression for Q factor

$$Q=\frac{wL_1}{R_1}=wC_4R_4$$

Advantages –

The two balance equations are independent if we choose $R_4$ and $C_4$ as variable elements

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

Disadvantages –

It requires a variable standard capacitor which may be very expensive if calibrated to the high degree of accuracy

It is limited to the measurement of low Q coils $(1\lt Q \lt10)$.