If your DC in supply is not too far away (distance/length not specified) you don't need a capacitor on the input. If your input supply is a small AC/DC walwart it will have a filter capacitor on its output. With a meter or so of cable you could probably do without the input capacitor on the regulator.
If your input supply is a small AC/DC walwart it will have a filter capacitor on its output. With a meter or so of cable you could probably do without the input capacitor on the regulator. You don't need an output capacitor BUT the transient response of the regulator will suffer.
The simple answer is, the capacitors are not required as long as the input is a clean DC and/or the load does not demand strict transient regulation. According to the datasheet, the two capacitors are required for the following reasons: C (in) is required if regulator is located at an appreciable distance from power supply filter.
According to the datasheet, the two capacitors are required for the following reasons: C (in) is required if regulator is located at an appreciable distance from power supply filter. C (out) "improves" stability and transient response.
Can a 7805 regulator be used without input/output capacitors First you should read a datasheet for the regulator such as this one. If your DC in supply is not too far away (distance/length not specified) you don't need a capacitor on the input. If your input supply is a small AC/DC walwart it will have a filter capacitor on its output.
An AC capacitor could be used for current limiting means in series, and if you used a 100 uF 350vac capacitor through an AC hot line at it's rated frequency, this would result in only 4 or 4.5 amps output because the cap could only allow this energy through as it functions in a very specific way in series.