The battery (3), which powers an apparatus (2), supplies an auxiliary circuit for a short time (5). A test and control component (6) of the device superimposes a low amplitude current interference .DELTA.i onto the discharge current (1). The interference signal frequency f is chosen acccording to the capacity and the discharge current of the battery (3). Processing of the frequency response of the battery (3) by the test and control component provides an indication of the combined impedence of the battery at that frequency. The value Z.sub.I =(.DELTA.V/.DELTA.I) sin (.DELTA..phi.) of the imaginary part of the impedence so measured, or advantageously the value of the quantity .GAMMA.=Z.sub.I.sup.-2 f.sup.-3/2 thereby indicates the state of charge of the battery.