Problem $2$: A coil having unknown resistance $\backslash ($ R x $\backslash )$ and inductance $\backslash ($ L x $\backslash )$ is shown in the circuit diagram of a simple Maxwell bridge. R$4$ and L$4$ represent a standard coil having known variable values. At balance, derive expressions for Rx and Lx in terms of known components R$2,$ R$3,$ R$4$ and L$4.($Hint$,$ at balance $\backslash (\backslash$boldsymbol$\{$Z$\}\_\{\backslash$boldsymbol$\{$x$\}\}\backslash$boldsymbol$\{$Z$\}\_\{3\}=\backslash$boldsymbol$\{$Z$\}\_\{2\}\backslash$boldsymbol$\{$Z$\}\_\{\backslash$mathbf$\{4\}\}\backslash ))$