A sensor for measuring a variable, in particular a physical variable, includes at least one converter element converting the variable into an electrical signal. At least one electronic signal processing unit conditions and/or processes the electrical signal to provide a sensor signal. The at least one electronic signal processing unit has at least one diagnosis device. An interface passes on the sensor signal through a connection, in particular a cable connection, to an electrical device, in particular a control device. The diagnosis device causes a fault signal instead of the sensor signal to be present at the interface when a fault occurs, for clearly distinguishing a fault at the interface from a processing fault. A circuit having such a sensor and a method for operating the sensor and the circuit are also provided.