written 7.8 years ago by | • modified 7.8 years ago |
Mumbai University > Electronics Engineering > Sem3 > Electronic Instruments and Measurements
Marks: 10M
Year: Dec 2014
written 7.8 years ago by | • modified 7.8 years ago |
Mumbai University > Electronics Engineering > Sem3 > Electronic Instruments and Measurements
Marks: 10M
Year: Dec 2014
written 7.8 years ago by | • modified 7.8 years ago |
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 $(1\lt Q \lt10)$.