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An amp is a standard measurement of electrical current - it's the current which flows when one volt is applied across a resistance of one ohm, and is given the symbol "I". Electrical power (in watts, but given the symbol "P") is given by multiplying voltage x current, or P=VI.

A car works on a 12volt system - the battery is 12v, so knowing that the headlamp bulbs and sidelight bulbs and everything else are 12volt, the lower power bits on a car (such as the 5watt sidelight bulbs) will take less current than the higher power bits (such as the 55watt headlamp bulbs - the 60watt main beams will take a bit more current). So in the fuse box you will find fuses with smaller current (amp) ratings for the lower-powered bits and higher amp ratings for higher powered bits. If the sidelights are all off one fuse, then the car is going to have at least four sidelight bulbs (4 x 5watts) and two number-plate illuminator bulbs of 5watts each, so 6 bulbs x 5watts gives a total load of 30w just for the sidelights. The current flowing through the fuse for this circuit would be I=P/V or 30 divided by 12 = 2.5amps. The fuse would perhaps be a 5amp or even a 10amp, so that it wouldn't just blow on the slightest pretext, like when a bulb blows.

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Q: Why are there different types of car amps?
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