A current measurement circuit includes first and second input nodes which receive the respective voltages at either side of a resistive element through which electrical current can flow, a differential amplifier means which produces an output signal indicative of the difference in voltage between its input terminals, electrical path forming means providing a connection between each of the input nodes and a respective input terminal of the differential amplifiers, a controllable voltage source for selectively applying an offset voltage to at least one input of the differential amplifier in response to a control signal, a control signal generator which generates the control signal applied to the voltage source such that at a first instance an offset voltage is applied which is greater than that applied at a second instance, and a diagnostic means which is adapted to identify faults present in the electrical path between the first input node and the respective input to the amplifier by comparing the output from the amplifier at the first instant when the offset voltage is applied and at the second instant without the offset voltage.