DC Circuits

EXAMPLE PROBLEM ON RESISTORS IN COMBINATION, CIRCUIT 2

Question
Figure 1 shows part of a circuit. It consists of resistors combined in both parallel and series configurations. Find the equivalent resistance.

Figure 1 Circuit 2, resistors in combination
    Hints
  1. What is the equivalent resistance for resistors in parallel?
  2. In series?

  3.  

Solution

In this partial circuit, there are three main branches, branch AB, branch CD, branch EF. As you can see, branch AB contains two resistors in series, R1 and R2. Branch CD has just one resistor, R3. Finally, there are two resistors in branch EF.

Let's look at branch AB first. We will simplify this branch by finding the equivalent resistance between A and B. Note that R1 is connected in series with R2. Using the equation for resistors in series


we can find RAB.

Now, in branch CD there is only one resistor, so this branch cannot be simplified further.

In branch EF, however, there are two resistors, connected in series with one another. Using the equation for resistors in series, we can find the equivalent resistance in branch EF, REF.


Figure 2 Circuit 2, simplified to a parallel circuit
We can redraw circuit 2 using RAB, R3, and REF, as seen in Figure 2. This circuit has been simplified to a parallel circuit, with three resistances in parallel. Using the formula for resistors connected in parallel
we can find the equivalent resistance of these branches.
Explanation on Resistors in Combination Circuits
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