Most aircraft require some form of electrical power to operate navigation-, taxi-, landing-, strobe lights, one or more COM and NAV radio's, transponder, intercom and other electronic systems. The electrical system consist of a battery and an alternator or generator on older aircraft. All of this is connected through several meters (kilometers in large aircraft) of wire.
All matter on earth is made up from molecules and they basically consist of atoms. These atoms are made of electrons, protons and neutrons. And electricity is about the flow of electrons attracted to protons and repelled by other electrons.
Alternators and generators generate a flow of electrons for us to make use of, but these items do nothing if the engine is not operating. To get them going we need some form of storage to be able to start up our engine so that electrical power can be generated.
For energy storage we take a look at another form thereof: capacitors use an electrostatic property. Where ordinary, everyday batteries use a chemical substance and reaction to store energy.
Where a standard battery delivers and takes in a charge rather slowly, supercapacitors can do this very quickly and without any degradation for millions of times even under extreme temperature conditions and vibrations. The reason for this behavior is their low internal resistance compared to a chemical battery. As such they can operate as a high performance buffer delivering high energy for short periods of time. Which is ideal for starting engines. These capacitors are not cheap but virtually indestructible and, like lithium batteries, light weight. To learn more about these components follow the next link to the Battery University.
The main difference between batteries and supercaps is the way energy is stored, their energy density and discharge profiles. Where the battery has relatively flat low voltage drop during discharge the supercap is a linear line down. This result in a large amount of energy being unused as the voltage is too low at that point for any device connected to it but there will still be a large amount of energy left. Read more about this discharge profile at the Battery University.
The capacity of a battery is expressed in Ah, amperes per hour. Theoretically, a battery of 35 Ah is capable of delivering 35 A for one hour or 1 A for 35 hours or any other combination. But it needs to be fully charged to be able to do that, hence the need for recharging during flight. A capacitor is expressed in Farads, which is equivalent to 1 Ampere second per volt or F = As / Volt. At 12 V, 1 Ah is equal to 300 F.
The energy (watt per second or Joule) stored in a capacitor is 1/2 C . V^2. For a battery it is Voltage x Capacity (in A-hr) x 3600 sec/hr.
Practical numbers for usable capacity in an engine start battery is about 20%, whereas a deep cycle AGM type can easily release 80% of its nominally rated capacity. Capacitors can deliver 100 %, but as said before, it is not a flat discharge profile.
Most modern aircraft use an alternator because these are able to deliver more power and are able to charge the battery with the engine idling, were the generator is unable to do that (less power per RPM) and has a heavier construction. The main design difference between these two is that an alternator has a rotating electromagnet (rotor) which is energized by the field current (ALT switch) and a stationary coil (stator) delivering the power.
The generator has a stationary permanent magnet and rotating coils within the fixed magnetic field generating the power through a commutator which rectifies the alternating voltage/current (AC) to direct voltage/current (DC). The alternator uses diodes to convert the AC to DC.
Both devices are voltage regulated and deliver 13,8 volts to the aircraft electrical system and they need an over-voltage protection and indicator for the pilot. Over-current protection is by design with an alternator but not in the generator, this one needs a separate current limiting device.
After the engine has started, the alternator (or generator) will provide the electrical power for the aircraft and recharges the battery. The battery is thus only needed to start the engine, supplementing the alternator in a high load situation and as an emergency source of power in case of engine or alternator failure.
The generator needs at least 1200 engine RPM to supply enough electrical power to recharge the battery, where the alternator can do that from idle RPM (below 900).
Some aircraft have a ground power receptacle, useful when testing the electrical system without running the engine and draining down the battery. Can sometimes also be used for starting the engine when battery capacity is not sufficient (cold weather). You will find a ground power switch near the master switch with a 'ground' and 'flight' mode. You have to make sure that the ground power unit is of the same voltage and polarity as the aircraft system.