DC Circuits
RESISTORS IN COMBINATIONCIRCUITS 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
Now, we can replace the two resistors with a single, equivalent resistor with no effective change to the circuit. 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
This gives: So, the equivalent resistance between points A and B is RAB. Replacing the parallel circuit between these two points with RAB gives the following circuit. Figure 4 Circuit 2, partially simplified. Figure 5 Circuit 2, simplified
Similarly, we can replace the parallel circuit containing R4 and R5 (between points C and D) with its equivalent resistance, RCD, where Replacing the parallel circuit between CD with its equivalent resistance yields the circuit in Figure 5 (above).

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: or
Rtotal = RAB + R3 + RCD
Here is an interesting animated exercise to help you with these concepts and Ohm's Law
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Press here  There are more complicated circuits which cannot be reduced to simply a parallel or series circuit using equivalent resistances. Instead, these need to be solved using to concepts: Kirchhoff's Current Law, and Kirchhoff's Voltage Law. Such complicated circuits will not be dealt with in this course, but are available in this tutorial. Example Problem on Resistors in Combination Circuits Self Test Return to: DC Circuits Menu Return to: Physics Tutorials Menu