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, 

Now, we can replace the two
resistors with a single, equivalent resistor with no effective change to the
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: 

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.


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
Use the "Back" button to return to this place when you are finished.
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
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