Here, we will combine series circuits and parallel circuits. These are
known as combination circuits. No new equations will be learned
here.
We can imagine a branch in a parallel circuit, but which contains two resistors in series. For example, between points A and B in Figure 1. In this situation, we could calculate the equivalent resistance of branch AB using our rules for series circuits. So, 
Figure 1 Combination Circuit 1 
Figure 2 Circuit 1 simplified to give a parallel circuit 
As can be seen in Figure 2, the circuit is now a parallel circuit, with resistors RAB and R3 in parallel. This circuit can be solved using the same rules as any other parallel circuit. (See Resistors in Parallel.) 
Another combination circuit can occur with parallel circuits connected in series. Figure 3 shows a typical example of two parallel circuits (AB and CD) connected in series with another resistor, R3.
Here, the resistors in the parallel circuit AB can be replaced by an
equivalent resistance. Again, we will use the equivalence rule for resistors
connected in parallel:

Figure 3 Combination Circuit 2 
Figure 4 Circuit 2, partially simplified. 
Figure 5 Circuit 2, simplified 
Now, you can see that we have simplified Circuit 2 to one which contains resistors connected in series only. That is, this circuit now contains RAB, R3, and RCD in series. The equivalent resistance for this circuit would be found using:
Example
Problem on Resistors in Combination Circuits
Self
Test
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