Q: Replacing 1.2v Ni-Cd battery with supercapacitor I have a trimmer which uses 1.2V 600 mah AA battery. Is it possible to replace it with a super capacitor ? Reason to replace is that the trimmer takes about 5-6 hrs to fully charge itself but the super capacitor (SC) can be charged in few seconds. 
I googled a lot ( and still trying to find ) if this was feasible and what specification SC I would need. From what I found I google I would need a SC with a voltage higher than charging voltage of trimmer so I guess 2.7v SC will be enough but how do I find how much Farad capacity  capacitor I would need ? Can I connect the SC directly to the positive and negative terminals where I insert the Ni-Cd battery ? Will I need any stabilizer or anything of such short to stabilise the output of capacitor. How long will the charge last ? Can it last enough so that the trimmer can do its job i.e. trim the beard ?

A: Lets assume your trimmer draws 600 mA while running thereby giving you a backup of 1 hour on full charge.
Resistance of trimmer = 1.2/0.6 = 2 ohms
Now lets assume the power is being provided by a supercap. Lets further assume that your trimmer will work in the voltage range of 1.4 V to 1.1 V without any issues and you would need a backup of at least 20 minutes so that you can shave after one charge.
Refer to the discharge formula given below:

Vc = 1 V
Vo = 1.4 V
R = 2 ohms
t = 20 mins = 1200 seconds
Calculation gives C = 2000 F.
Yes, that's farads.
So, lets talk about feasibility. Here is a 2000 F capacitor from digikey:

This has a dia of 6 cm and height of 10 cm and costs 56 USD.
If this size and price point is okay with you, you can go ahead :)
Edit : Corrected capacitor specs.

A: No, you can't.
The reason is: The accumulator has a non-linear voltage drop. While discharging, the voltage remains the same for a longer period of time.
The SC has a linear voltage drop. As soon as discharging starts, the voltage drops at a constant rate. You will not be able to use all stored energy, since as soon the voltage drops below the nominal voltage of the trimmer everything stops working.
You may be able to combine a LOT of SCs (mixed parallel & serial) with a buck/boost converter -- but all this converting will burn a lot of electrical energy and all the SCs costs a lot of money and the thing will be more like
a tank than anything else. ;)

A: I'll answer your last question first, because it's the only one that really matters:

Can it last enough so that the trimmer can do its job i.e. trim the beard ?

Probably not. At least, not while still fitting into the device.
Supercapacitors have much lower energy density than batteries. They can charge and discharge much faster than a battery, but they cannot store anywhere near as much power in total.
Whether it will work on an electrical level will depend on the specific design of the device. That's not something we can necessarily answer.
