The power supply includes an output unit that converts a DC voltage and outputs the DC voltage; a capacitor that stabilizes the DC voltage output from the output unit, the power supply being able to be operated in a power saving mode in which a power consumption is reduced by stopping a whole or part of an operation of a load operated by the DC voltage output from the output unit; a detection unit that detects that a power is cut off; a discharging load that discharges the capacitor; and a control unit that performs control so as to operate the charging load when the detection unit detects that the power is cut off during the operation in the power saving mode.