Okay so the current drawn through the switch will not be determined by the capacity of the power supply ...
Capacity of the power supply has
nothing at all to do with the amount of current that is delivered by the power supply. This concept is so basic to the understanding of electricity that you should limit yourself to "playing" only with a handful of low-voltage cells (AA or otherwise) until you fully grasp its significance and importance.
The capacity of a battery (or cell) to deliver power to a circuit is defined by its energy storage capability at a given (specified) terminal voltage. It is expressed in ampere-hours (AH) or milliampere-hours (mAH). Thus a 12 V DC battery consisting of eight 1.5 V DC "AA-size" cells connected in series can theoretically supply anywhere from 1000 to 3000 mAH of energy, depending on battery construction. That could be one ampere for one hour (1000 mAH) or up to three amperes for one hour (3000 mAH) or various combinations of current multiplied by time that do not exceed the mAH specification... within certain practical limits.
You might, for example, expect an AA battery stack to be able to deliver one ampere (1000 mA) for one hour, with 12 V DC terminal voltage, with a rated capacity of 1000 mAH. That would be 12 W of power (12 V x 1 A) dissipated over a period of one hour (3600 S) and require (12 W) x (3600 S) = 43200 watt-seconds or 43.2 kJ of energy. Some "AA-size" cell chemistries may actually support this rate of power dissipation.
But you cannot expect an AA battery stack to deliver
ten times the current for
one tenth the time (ten amperes for one tenth of an hour or six minutes) even though the ampere-hours are identical.
Nor one hundred times the current for
one hundredth the time (one hundred amperes for one hundredth of an hour or thirty-six seconds).
Nor one thousand times the current for
one thousandth the time (one thousand amperes for three point six seconds),
The ampere-hours is the same in all these examples, but the internal construction of the AA cell just isn't capable of supplying the increased current while maintaining the 12 V DC terminal voltage. Other cell chemistries will give different results. For example, lithium-ion cells provide insanely large discharge currents in a small volume package. Lead-acid cells also provide large discharge currents for short periods of time, several hundred amperes at twelve volts for automobile starter applications, for example.
The point is this: ampere-hour (or milliampere-hour) ratings provide a means to compare battery capacities under certain defined discharge conditions, but the actual discharge capacity depends on other factors besides current drawn from the battery and the amount of time the current is drawn. However, in all instances the current delivered by the battery depends only on the load resistance, not the battery capacity. Operating a 1000 mAH battery at 100 mA of current would theoretically allow ten hours of discharge time, but your mileage (or kilometers) may vary depending on temperature and how low the terminal voltage can go before you consider the battery to be fully discharged.
