EXAMPLE PROBLEM ON RESISTORS IN COMBINATION CIRCUITS

Question Figure 1 Combination Circuit 1

Hints Which resistors are in parallel and which are in series? Is this circuit composed of small groups of parallel resistors, all connected in series? Or is it composed of groups of series resistors, connected in parallel?

Solution
This circuit is composed of 3 'elements' connected in series: the group of parallel resistors between A and B, the single resistor R3, and the group of parallel resistors between C and D.

First, we will find the equivalent resistance between A and B.
Here, we have two resistors, R1 and R2, connected in parallel. Using the formula for resistors connected in parallel:

Replacing the two parallel sections with their equivalent resistances, and redrawing the circuit, we get the circuit in Figure 2. We see that there are three resistances connected in series: RAB, R3, and RCD. Using the formula for resistors in series,  we can find the equivalent resistance of the circuit.

Figure 2 Simplified Version of Circuit 1