Three resistors in parallel

Question: What happens if we have three or more resistors in parallel?

Solution: This is an important example, because the solution involves an important technique for understanding circuits: breaking them down into smaller parts and them simplifying those parts. In the circuit (a), with three resistors in parallel, we can think of two of the resistors as forming a single big resistor, (b), with equivalent resistance

We can then simplify the circuit as shown in (c), so that it contains only two resistances. The equivalent resistance of the whole circuit is then given by

Substituting for R_{1 and 2} and simplifying, we find the result

which you probably could have guessed. The interesting point here is the divide-and-conquer concept, not the mathematical result.