Current sensor and battery with current sensor

The invention provids a current sensor and a battery with current sensor. The current sensor includes a magnetic detection element having a resistance value changed by applying inductive magnetic field from measurement target current, a magnetic core provided in the vicinity of the magnetic detection element, and a coil generating magnetic field attenuating the inductive magnetic field. A constant level current in a predetermined range of output voltage of the magnetic detection element flows in the coil, and the measurement target current is detected on the basis of the output voltage of the magnetic detection element.