In a circuit arrangement for measuring currents at high potential, a capacitor, charged in accordance with the current to be measured, is shunted by a light emitting diode which generates a light pulse sequence with a frequency proportional to the current. In series with the diode is a switching element with a control terminal, to which the output of a control device is connected. The input of the control device is connected to a threshold arrangement disposed parallel to the capacitor and the supply terminals of the control device are connected to the capacitor.