A low frequency AC resistance bridge, suitable for high resolution measurements on small resistances, is described. A precision of 0.01% can be obtained down to the milliohm range with a sample current of 10 mA. A special current comparator is used to automatically keep a constant ratio between the sample current and the current through the balancing decade resistor. The sample current may be up to ten thousand times larger than the current through the decade resistor. The two currents are kept in phase via optical coupling.