Electrical system comprising: - terminals (V+, V-) able to be connected to an onboard electric power source designed to deliver a voltage between these terminals; - a circuit for detecting an electrical insulation fault between the electrical power source and a body forming a floating electrical ground, an insulation fault corresponding to an abnormal resistance value in at least one insulation resistance (Ri) between the body and at least one point of the electrical power source, - a device for measuring a current; - a control unit ; characterized in that the detection circuit further comprises a controllable voltage generator , connected to said body and to a single first terminal from among said terminals and designed to bias the body and the single first terminal at different potentials; and in that the device for measuring a current is configured to measure a current incoming onto said first terminal and outgoing across said at least one point of the source, this current subsequently flowing through said at least one insulation resistance to said body; the control unit is configured to: o control the application, by said programmable voltage generator, of at least one non-zero voltage value between the body and the single first terminal, o acquire at least one value of the current measured by said measurement device for each applied voltage value; o calculate a value of at least one insulation resistance based on said at least one measured value of the current. - terminals (V+, V-) able to be connected to an onboard electric power source designed to deliver a voltage between these terminals; - a circuit for detecting an electrical insulation fault between the electrical power source and a body forming a floating electrical ground, an insulation fault corresponding to an abnormal resistance value in at least one insulation resistance (Ri) between the body and at least one point of the electrical power source, - a device for measuring a current; - a control unit ; characterized in that the detection circuit further comprises a controllable voltage generator , connected to said body and to a single first terminal from among said terminals and designed to bias the body and the single first terminal at different potentials; and in that the device for measuring a current is configured to measure a current incoming onto said first terminal and outgoing across said at least one point of the source, this current subsequently flowing through said at least one insulation resistance to said body; the control unit is configured to: o control the application, by said programmable voltage generator, of at least one non-zero voltage value between the body and the single first terminal, o acquire at least one value of the current measured by said measurement device for each applied voltage value; o calculate a value of at least one insulation resistance based on said at least one measured value of the current. o control the application, by said programmable voltage generator, of at least one non-zero voltage value between the body and the single first terminal, o acquire at least one value of the current measured by said measurement device for each applied voltage value; o calculate a value of at least one insulation resistance based on said at least one measured value of the current. <EOS>