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2) Electrical Power

Power is equal to current times voltage: P=VI and has a unit of Watts
Another, really simple equation... and yes it works and is used constantly to ensure proper sizing.
The equation determines the way that we measure an electrical systems ability to do work. 

500 Watts(DC) = 1V @500Amps
500 Watts(DC) = 2V @250Amps
500 Watts(DC) = 20V @25 Amps
500 Watts(DC) = 2000V @ .25Amps

(DC means Direct Current, power is always the "area under the curve" of voltage*current)
Audio Amplifiers are rated with RMS and peak values... (More to come)

The power stays the same,500W, for various voltages and currents and that gives design choices for various systems. 

Current determines the size of conductor needed  higher current requires bigger(more expensive) wires.

Voltage is typically determined by the system(battery, generator, turbine). Higher voltage requires more insulation and spacing to contain(Isolate from the environment and earth ground) the electric potential.

You can use Ohms law, V=IR, to transform the Power equation P=VI:
From Ohms law we know:
Current Power Transformation

Typically, I approach power ratings by solving for the current through the known resistance and then use this formula.

The other version is the Voltage Power

Voltage Power Transform
I use this form when calculating required voltage rails to deliver power to a known load like a resistor.

Power draw is a major factor for determining if something is practical. Putting a 4 ohm load on a battery is going to drain the battery very quickly. Delivering power to a 4ohm speaker involves a power amplifier and is purpose driven.

So how do voltage and current relate when there isn't a physical resistor? 

The answer is that "active" devices work on currents drawn from a fixed voltage supply. 
Active devices are devices who's operating parameters can be changed electrically. 
A transistor is an active device.( 
Resistors, Capacitors and Inductors are passive devices.