Mathematical Relationship between various quantities in an electrical circuit:
Ohm's Law: E=IR; where -
- E = Voltage (Volts)
- I = Current (Amperes)
- R = Resistance (Ohms)
Watt's Law: P = IE; where -
- P = Power (Watts)
- I = Current (Amperes)
- E = Voltage (Volts)
Both of these equations may be re-arranged individually or combined as needed, using standard rules of algebra.
It should be borne in mind that the nominal system voltage for light automotive applications is +12.0VDC, while actual voltage runs closer to +13.0-13.5VDC. Using +12.0VDC as a standard value for E will provide a small but useful safety margin in figuring current, and you use that figure for fusing and wiring selection.
Let's take your lamps for a moment - we'll presume they're a pair of 55W lamps (driving or fog, doesn't matter):
55W + 55W = 110W. 110W = EI = 12I. E = 110W/+12VDC = 9-1/6A. Therefore, protect the circuit with a 10A fuse, use a relay capable of handling up to 10A, and select wiring with a minimum ampacity for distance of 10A. (The switch you use to trip the relay need only carry 100-150mA, since that's the given current to "make" on a DIN relay.)
To illlustrate the "safety margin" that is inbuilt with using 12VDC as a nominal figure, we'll recalculate at a measured 13.4VDC:
110W/12VDC = 9-1/6A
110W/13.4VDC ~=8.209A
While this isn't significant at this relatively low current rating, it can add up and give you a warm fuzzy feeling, knowing you're covered, with larger loads. Therefore, it's a good habit to get into.
Ohm's Law and Watt's Law are simple formulae that all mechanics (professional or amateur) who work with vehicle electrics should have either burned into their brains or tattooed on the inside of their eyelids.