Series-RL parallel-RC bridge balance ($R_1=R_2{R}_3/R_4,L_1=R_2{R}_3{C}_4$)

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.

With other arms fixed and a high-input-resistance detector, the DC midpoint difference has derivative $-V_s{R}_2/(R_1+R_2{)}^2$ with respect to $R_1$. Dividing a small detectable voltage change by its magnitude gives the local resistance resolution. Calibration, source stability, thermal drift and detector loading contribute separately to total measurement uncertainty. Detector sensitivity alone is not a complete accuracy claim.