 Series-RL parallel-RC bridge balance

An unloaded four-arm resistance bridge with $Z_1=R_1+i\omega L_1$ and $Z_4=R_4/(1+i\omega R_4{C}_4)$ balances when $Z_1{Z}_4=R_2{R}_3$. Multiplying through the RC denominator and comparing real and imaginary coefficients gives the displayed conditions. In this ideal model they hold at all frequencies, including the DC steady limit. Replacing the parallel RC arm by a series arm changes the balance law.