Parallel Circuits

Which becomes:

So there is a little more than one-half ohm resistance in the circuit. You can see that the more resistors in parallel, the less the resistance.

In fact, the total resistance is always less than the smallest resistor. This is why a fuse will blow if you add too many circuits to the fuse. There are so many paths for the current to follow that the total resistance of the circuit is very low. That means the current is very high - so high that the fuse can no longer handle the load.

B. For two resistors:

Parallel circuits are a different story. In a parallel circuit, there are three ways to find total resistance. Method A works in all cases. Method B works only if there are two branches, equal or not. Method C works only if the branches are of equal resistance.

A. The total resistance is equal to one over the sum of the reciprocals of the individual resistors. That sounds confusing, but looking at the formula will make it clearer:

For a 3 ohm and a 5 ohm resistor that would be:

C. For several identical resistors, divide the value of one resistor by the number of resistors, or:

PARALLEL:

n example will make it even clearer. Suppose there is a circuit with three resistors in parallel: 4 ohms, 2 ohms, and 1 ohm. The formula would look like this:

Where R1 is the value of one resistor and n is the number of resistors. So if you had three 4 ohm resistors in parallel it would be:

For a 3 ohm and a 5 ohm resistor that would be:

PARALLEL: