Current is sensed by a circuit which provides a high frequency reversing voltage to a sensing winding on a current transformer, for driving the transformer into its linear region once per cycle of applied voltage. Current through the sensing winding is sampled while the transformer is in that linear region. After taking a current sample application of the reversing voltage, sensor power consumption is reduced by inhibiting the application of voltage to the sensing winding for one or more of the high frequency cycles, or the same control and sensing circuitry is used to cause application of reversing voltage to a sensing winding on a different transformer measuring current through a different conductor, such as in a polyphase arrangement or for monitoring ground fault current. Preferably, the current is sampled approximately at the instants of reversal of the voltage being applied to the sensing winding, and the sample having the lower absolute value is selected as a sample proportional to the line current.