Series/Parallel Reduction of Resistor Networks
There are some occasions where a complex network of resistors is encountered. While a bruteforce solution is possible, it is advantageous to first reduce the resistor network. By repeatedly
using the equations for resistors in series and parallel, the network can be simplified.
The procedure is simple. Find pairs of resistors in the network that are in parallel or in series.
Replace the pair with the equivalent resistance as defined by the equation for series or parallel
resistors. Repeat the reduction process until a single equivalent resistance is found.
The difficulty comes in correctly identifying parallel or series connected resistors. Remember
that two resistors are not in series if another component is connected at their common junction.
Resistors are not in parallel unless both of their terminals are connected to the same nodes. It is
easy to be fooled by the schematic diagram. Two resistors drawn in parallel may or may not be in
an electrically parallel configuration.
4
6
A
The 6 and 18 ohm resistors
are replaced by one equivalent
resistance that is connected to
the same place in the circuit.
10
20
A
A
3
6
6
18
24
B
B
B
The 6 and 24 ohm resistors
are replaced by one equivalent
resistance that is connected
to the same place in the circuit.
4
A
A
10
4
4.8
B
Figure 1: A Simple Network to Reduce
3
B
The two 4 ohm
resistors are
D
Consider the network above. In the first step we notice that the 6 ohm and 18 ohm resistors are in
series. We can thus replace them with one resistor of 24 ohms. Now we see that the 6 and 24 resistors are in parallel. Using the equation for resistors in parallel gives us the equivalent resistance
A
between terminals A and B to be:
10
Req = (6 ∗ 24)/(6 + 24) = 4.8Ω
10
Two
3
1
B
TITLE
Now let’s tackle a more complex network. The solution is shown schematically step by step.
4
4
A
A
10
6
2
20
24
5
B
3
20
2 ohm and 1 ohm
resistors are in series
3
6
6
10
A
1
3
5
B
6 ohm and 3 ohm
resistors are in parallel
4
B
4
A
A
2
10
4
4.8
20 ohm and 5 ohm
resistors are in parallel
2
10
20
C
3
3
B
5
B
The two 4 ohm and 2 ohm
resistors are in series
D
A
A
10
3
10
5
E
The 10 and 3 ohm
resistors are in series
Two 10 ohm resistors
are in parallel
B
F
3
B
Figure 2: A Bigger Network to Reduce
TITLE
FILE:
PAGE
REVISION:
OF
DRAWN BY:
2
A
8
B