Power rating

All resistors are given a specification that determines how much power they can safely dissipate. Typical values are 1/4W, 1/2W, and 1 W. Units also exist with ratings of 1/8W or 2 W. These dissipation ratings are for continuous duty.
You can figure out how much current a given resistor can handle, by using the formula for power (P) in terms of current (I) and resistance (R): P = I ²R. Just work this formula backwards, plugging in the power rating for P and the resistance of the unit for R, and solve for I. Or you can find the square root of P/R. Remember to use amperes for current, ohms for resistance, and watts for power.
The power rating for a given resistor can, in effect, be increased by using a network of 2 × 2, 3 × 3, 4× 4, etc., units in series-parallel. You’ve already learned about this. If you need a 47-ohm, 45-W resistor, but all you have is a bagful of 47-ohm, 1-W resistors, you can make a 7 × 7 network in series-parallel, and this will handle 49 W. It might look terrible, but it’ll do the job.
Power ratings are specified with a margin for error. A good engineer never tries to take advantage of this and use, say, a 1/4-W unit in a situation where it will need to draw 0.27 W. In fact, good engineers usually include their own safety margin. Allowing 10 percent, a 1/4-W resistor should not be called upon to handle more than about 0.225 W. But it’s silly, and needlessly expensive, to use a 2-W resistor where a 1/4-W unit will do, unless, of course, the 2-W resistor is all that’s available.