An apparatus for measuring the local electrical resistance of a surface, the apparatus comprising: - a conductive probe suitable for coming into contact with a surface of a sample to be characterised; - a measurement circuit connected to the conductive probe in order to generate a signal representative of a contact resistor (Rx) between said conductive probe and said surface of the sample; - a DC voltage source for applying a bias voltage (Vpol); and - a control device connected to the measurement circuit for controlling said measurement circuit; the measurement circuit comprising a resistive measurement dipole having stepwise variable resistor and connected between said conductive probe and a ground of the circuit, such that the contact resistor and the resistive measurement dipole form a voltage divider, said resistive measurement dipole comprising a plurality of measurement resistors (RM1, RM2) of decreasing resistances, at least one of which may be connected or disconnected selectively between said conductive probe and ground; wherein the DC voltage source is configured to apply the bias voltage (Vpol) to said sample; wherein the device further has a calculation unit for generating said signal representative of the contact resistor (Rx) between said conductive probe and said surface of the sample as a function of a voltage (Vs) which appears across the terminals of said measurement resistive dipole as a consequence of applying said bias voltage (Vpol); and in that said control device is adapted to modify the resistance value of said resistive dipole in accordance with a control law with hysteresis as a function of a previously measured value of said contact resistor (Rx) so as to match the measurement range of the apparatus to the resistor to be measured. - a conductive probe suitable for coming into contact with a surface of a sample to be characterised; - a measurement circuit connected to the conductive probe in order to generate a signal representative of a contact resistor (Rx) between said conductive probe and said surface of the sample; - a DC voltage source for applying a bias voltage (Vpol); and - a control device connected to the measurement circuit for controlling said measurement circuit; the measurement circuit comprising a resistive measurement dipole having stepwise variable resistor and connected between said conductive probe and a ground of the circuit, such that the contact resistor and the resistive measurement dipole form a voltage divider, said resistive measurement dipole comprising a plurality of measurement resistors (RM1, RM2) of decreasing resistances, at least one of which may be connected or disconnected selectively between said conductive probe and ground; wherein the DC voltage source is configured to apply the bias voltage (Vpol) to said sample; wherein the device further has a calculation unit for generating said signal representative of the contact resistor (Rx) between said conductive probe and said surface of the sample as a function of a voltage (Vs) which appears across the terminals of said measurement resistive dipole as a consequence of applying said bias voltage (Vpol); and in that said control device is adapted to modify the resistance value of said resistive dipole in accordance with a control law with hysteresis as a function of a previously measured value of said contact resistor (Rx) so as to match the measurement range of the apparatus to the resistor to be measured. the measurement circuit comprising a resistive measurement dipole having stepwise variable resistor and connected between said conductive probe and a ground of the circuit, such that the contact resistor and the resistive measurement dipole form a voltage divider, said resistive measurement dipole comprising a plurality of measurement resistors (RM1, RM2) of decreasing resistances, at least one of which may be connected or disconnected selectively between said conductive probe and ground; wherein the DC voltage source is configured to apply the bias voltage (Vpol) to said sample; wherein the device further has a calculation unit for generating said signal representative of the contact resistor (Rx) between said conductive probe and said surface of the sample as a function of a voltage (Vs) which appears across the terminals of said measurement resistive dipole as a consequence of applying said bias voltage (Vpol); and in that said control device is adapted to modify the resistance value of said resistive dipole in accordance with a control law with hysteresis as a function of a previously measured value of said contact resistor (Rx) so as to match the measurement range of the apparatus to the resistor to be measured.