An invasive device which is intended to cooperate with a magnetic resonance imaging apparatus is provided with an RF coil which is situated near a distal part of the invasive device. The RF coil is used so as to visualize the position of a distal end of the invasive device, introduced into an object, in an image of the object. Current induced by an RF field to be generated by the magnetic resonance imaging apparatus develops heat in the electric connection between the RF coil and a control unit, which may be annoying to a patient. In order to counteract the development of heat in the invasive device, the invasive device is provided with a hollow carrier. The electric connection extends through said carrier which is provided with an electrically conductive shield with an additional resistance.