## Ohm's Law

If there is one math formula you should know to build up your system, it'll be Ohm's law. In its most basic form, it gives the relation between voltage, current and resistance:

V = I x R

- V = voltage (sometimes you will see U instead of V as a symbol)
- I = Current (in Ampere, or Amp)
- R = resistance (in Ohm, symbol Ω)

The reason this formula is important is because it is related to how power is transmitted and how one can do that efficiently. It also explains why losses appear in the cable and why increasing the voltage lowers those losses. First, we take a look at the resistance of a wire. This is calculated as follows:

R = rho x L / S

where:

- R = resistance of the wire
- rho = specific resistivity of the material (symbol: ρ)
- L = length of the wire
- S = cross section of the wire

The important thing to know from this is that the thinner the wire, the higher the resistance and the longer the wire, the higher the resistance. Thus it is important to use cable that is as thick and as short as possible to minimize losses.

Finally, power is given by:

P = V x I

or in case we rewrite this since: V = I x R

P = R x I x I = R x I^2

Putting these all together we can see that in order to minimize losses in the resistance of the wire we have (and besides keeping cable runs short and tick) we should keep the current as low as possible since this generates losses in the cable (heat) to the rate of I^2. Since the relation between voltage and current is given by Ohm's law, we know that for the same resistor of the wire and for the same amount of power transfer, we can increase the voltage which will decrease the amount of current. Lower current means we can use thinner wire as well, which ends up saving costs.