A sensor is provided including: an element outputting detection signals according to magnitude of physical quantity; a drive circuit outputting a driving signal to the element and receiving a monitor signal from the element; a detection circuit that includes amplifiers amplifying the detection signals and a first synchronous demodulation circuit performing synchronous demodulation on a signal from the amplifier, receives the detection signals, and outputs a physical quantity signal according to the physical quantity; a processing circuit processing a signal from the first synchronous demodulation circuit; a first diagnostic circuit that receives a signal into the processing circuit and a signal from the processing circuit, and outputs a first error signal when abnormalities occur in the processing circuit; and a second diagnostic circuit that outputs a diagnostic signal to the first diagnostic circuit, instead of the signal into the processing circuit or instead of the signal from the processing circuit.