Current is flowing charge. Like water in a hose, which flows due to a difference in pressure from one end to the other, current flows due to a voltage difference. Voltage is sometimes called electrical pressure because of this similarity.
You need Ohm's law, I = D V/R or D V = IR, where I is current through resistance R and D V is voltage across it. From now on we drop the D for simplicity. Since conventional current goes from + to - by definition, if you travel in the direction of current through a resistor, the voltage drops, so we should say V = -IR, but the conventional way to say it is just V=IR.
Series and parallel equations, Rs = S R and Rp = 1/S (1/R) are easily derived by noting that series resistors carry the same current, and parallel resistors have the same voltage across them. In your head (or on paper) you can then replace a group of resistors with a single R.
The parallel R formula is not needed unless you are dealing with a combination of series and parallel. For example, if R1 = 2 W , R2 = 3 W and R3 = 4 W , and they are all connected in parallel to a 12 V car battery, each current can be calculated separately: 6 A, 4 A, and 3 A, respectively, for a total of 13 A. We could have found Rp = 12/13 W , then I = 12/(12/13) = 13 A, but the first method is easier.
Try some series-parallel combinations:
Call them circuit A, B and C, respectively. In circuit A, if R1 = 10 W , R2 = 20 W , R3 = 30 W and R4 = 40 W , what is Rtotal?
In circuit B, same R values as above, and R5 = 50 W . Find total R.
In circuit C, same R values; find total R.
(The answers are 62W , 66W , and 35.5W , respectively.)
For more fun, call the battery voltage 1.5 V, and calculate all the currents and voltage drops. In each of circuits A and B, there are two resistors which carry the entire battery current. This will get you started, and when you get sick of that, mosey on back to the main page on electricity and stuff. Or if you want to get into circuits which cannot be analyzed by series and parallel, hit beyond series & parallel. Chances are, you don't need to go beyond series and parallel, so stay away from it.
Here is an interesting circuit—the length of the chain does not matter, the resistance from A to B is 2 W if all the horizontal ones are 1 W each and the vertical ones are 2 W except the last one, 1 W.
A 1 1 1 1 1
2 2 2 2 1 W
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Comments, questions: fredrick.gram at tri-c.edu (remove spaces and replace at with @.