SSC JE Electrical Engineering 2015 Paper

A maxwell bridge is a modification to a wheat store bridge used to measure an unknown inductance (usually of low Q) in terms of calibrated Resistance and inductance or Resistance and Capacitance. The balance condition for maximum bridge is given as
${\mathit{Z}}_1{\mathit{Z}}_4={\mathit{Z}}_2{\mathit{Z}}_3$
${\mathit{Z}}_1={\mathit{R}}_{\mathit{x}}+\mathit{j}\mathit{\omega }{\mathit{L}}_{\mathit{x}}$
${\mathit{Z}}_2=200\mathit{\Omega }$
${\mathit{Z}}_3=750\mathit{\Omega }$
${\mathit{Z}}_4={\mathit{R}}_4\mid \mid \left(\mathit{j}\mathit{\omega }{\mathit{C}}_4\right)$ $=4000\mid \mid \frac{1}{\mathit{j}\mathit{\omega }\left(0.5\times {10}^{-6}\right)}$
$\left({\mathit{R}}_{\mathit{x}}+\mathit{j}\mathit{\omega }{\mathit{L}}_{\mathit{x}}\right).\frac{4000+\frac{1}{\mathit{j}\mathit{\omega }\times 5\times {10}^{-8}}}{\left(4000\times \frac{1}{\mathit{j}\mathit{\omega }\times 5\times {10}^{-8}}\right)}$ $=2000\times 750$
${\mathit{R}}_{\mathit{x}}=\frac{200\times 750}{4000}=3754$
${\mathit{L}}_{\mathit{x}}=200\times 750\times 5\times {10}^{\mathit{–}8}=75\mathit{m}\mathit{H}$