total current is known. If the total current is not known, other means
must be used for finding the total resistance.
The simplest case is
that of several equal resistors connected in parallel.
To solve this
problem, divide the resistance of one piece of equipment by the number
of pieces connected in parallel. If two 10-ohm resistors are connected
in parallel, the total resistance offered by the two is 10/2, or 5
ohms.
If three 12-ohm resistors are connected in parallel, the total
resistance offered by the three resistors is 12/3, or 4 ohms. In other
words, the total resistance of equal resistances connected in parallel
is equal to one resistance divided by the number connected.
(2) Unfortunately, the different pieces of equipment used in electrical
circuits do not have the same resistances. Therefore, they do not all
draw the same amount of current when different pieces of equipment are
connected across a battery.
For such cases, another method has been
found for the calculation of the total resistance. Refer to figure 6
which shows two resistors of unequal value placed in parallel across a
battery.
Figure 6.
Two unequal resistors connected in parallel.
(3) The most commonly used method of determining the resistance of a
parallel circuit is known as the product-over-the-sum method as is
shown below.
6.
SERIES-PARALLEL CIRCUITS
Series-parallel circuits consist of groups of parallel resistors in series
with other resistors.
a. Solving Series-Parallel Circuits. Series-parallel circuits may be solved
by application of the rules already given for simple series and simple parallel
circuits.
To do this, the series-parallel circuit is reduced to an equivalent,
simplified circuit.
Each group of parallel resistors is first replaced by its
equivalent single resistance, and then the entire circuit is treated as a series
circuit. Refer to figure 7.
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