Page 96 - Teach Yourself Electricity and Electronics

76 Basic dc circuits

Sometimes, the total resistance of a series-parallel network is the same as the value
of any one of the resistors. This is always true if the components are identical, and are
in a network called an n-by-n matrix. That means, when n is a whole number, there are
n parallel sets of n resistors in series (A of Fig. 4-10), or else there are n series sets of n
resistors in parallel (B of Fig. 4-10). Either arrangement will give exactly the same re-
sults in practice.

4-10 Series-parallel combinations. At A, sets of series resistors are
connected in parallel. At B, sets of parallel resistors are in series.

Engineers and technicians sometimes use this to their advantage to get resistors
with large power-handling capacity. Each resistor should have the same rating, say 1 W.
2
Then the combination of n by n resistors will have n times that of a single resistor. A 3
2
3 series-parallel matrix of 2-W resistors can handle 3 2 9 2 18 W, for ex-
ample. A 10 10 array of 1-W resistors can take 100 W. Another way to look at this is to
see that the total power-handling capacity is multiplied by the total number of individ-
ual resistors in the matrix. But this is only true if all the resistors have the same ohmic
values, and the same power-dissipation ratings.
It is unwise to build series-parallel arrays from resistors with different ohmic values
or power ratings. If the resistors have values and/or ratings that are even a little nonuni-
form, one of them might be subjected to more current than it can withstand, and it will
burn out. Then the current distribution in the network can change so a second