Question

The Maxwell's bridge shown in the figue is at balance. The parameters of the inductive coil are

• A. $R=R_2{R}_3/R_4,L=C_4{R}_2{R}_3$
• B. $L=R_2{R}_3/R_4,R=C_4{R}_2{R}_3$
• C. $R=R_4/R_2{R}_3,L=1/\left(C_4{R}_2{R}_3\right)$
• D. $L=R_4/R_2{R}_3,R=1/\left(C_4{R}_2{R}_3\right)$

Answer 1

The correct option is A $R=R_2{R}_3/R_4,L=C_4{R}_2{R}_3$


$Z_1=R+j\omega L;Z_2=R_2;Z_3=R_3$

$Z_4=R_4||\left(\frac{-j}{\omega C_4}\right)$

$=R_4||\left(\frac{1}{j\omega C_4}\right)=\frac{R_4}{1-j\omega C_4{R}_4}$

At balance,

$Z_1{Z}_4=Z_2{Z}_3$

$(R+j\omega L)\left(\frac{R_4}{1+j\omega C_4{R}_4}\right)=R_2{R}_3$

$R_4(R+j\omega L)=R_2{R}_3(1+j\omega C_4{R}_4)$

$R{R}_4+j\omega L{R}_4=R_2{R}_3+j\omega R_2{R}_3{R}_4{C}_4$

Equating real and imaginary terms,

$R{R}_4=R_2{R}_3$

$R=\frac{R_2{R}_3}{R_4}$

$\omega L{R}_4=\omega R_2{R}_3{R}_4{C}_4$

$L=R_2{R}_3{C}_4$