Most circuits in electrical equipment are not series or parallel circuits.
They are usually seriesparallel circuits, which are combinations of series
and parallel circuits. A seriesparallel circuit consists of groups of
parallel resistors connected in series with other resistors. An example
of a seriesparallel circuit is shown in figure 864.
The requirements for a seriesparallel circuit are as follows: (1) power source (battery).

While seriesparallel circuits may appear extremely complex,
the same rule used for series and parallel circuits can be applied to simplify
and solve them.
The easiest method of handling seriesparallel circuits is to break them apart and redraw them as equivalent circuits. The circuit in figure 865 is an example of a simple seriesparallel circuit that can be redrawn to illustrate this procedure. In this circuit the same voltage is applied to R2 and R3; thus they are in parallel. The equivalent resistance of these two resistors is equal to the value of one resistor divided by the number of resistors in parallel. This is true only when the parallel resistors have the same ohmic value. If this rule is applied, the circuit can be redrawn as shown in figure 866. 
This has converted the original seriesparallel circuit into a simple
series circuit containing two resistances. To further simplify the circuit,
the two series resistances can be added, and the circuit can be redrawn
as shown in figure 867.
Although the last redrawing of the circuit could have been
omitted and the calculations done mentally, this circuit illustrates clearly
that one 25 ohm resistor is the resistive equivalent of the three resistors
of the original circuit. Figure 868 contains a more complex seriesparallel
circuit.
The first step in simplifying this circuit is to reduce each group of parallel resistors to a single equivalent resistor. The first group is the parallel combination of R2 and R3. Since these resistors have unequal values of resistance, the formula for two parallel resistances is used: 
Then the parallel combination of W
resistor, as shown in figure 869.
Next, the equivalent resistance of the parallel combination
of can be determined using
the formula = R/N: where,
is the equivalent resistance of R4, R5, and R6, R is the value of one of
the resistors, and N is the number of resistors in parallel,
The parallel combination of R4, R5, and R6 can now be redrawn as a single 20 ohm resistor, as shown in figure 870. The original seriesparallel circuit has now been replaced with its equivalent series circuit. This circuit could be redrawn again to replace the five resistors in series with one 330 ohm resistor. 
This can be proved by using the total resistance formula for series circuits:
The first seriesparallel circuit used is redrawn to discuss the behavior
of current flow (figure 871).
Unlike the parallel circuit, the branch currents, I1 and I2, cannot be established using the applied voltage. Since R1 is in series with the parallel combination of R2 and R3, a portion of the applied voltage is dropped across R1. In order to find the branch currents, total resistance and total current must be found first. Since R2 and R3 are equal resistance, 
Total resistance is
Using Ohm's law, total current is
The total current, 1 ampere, flows through R1 and divides
at point A, with part of the current flowing through R2, and the other
part through R3. Since R2 and R3 are of equal size, it is obvious that
half of the total current, or 0.5 amps, will flow through each branch.
The voltage drops in the circuit are determined by Ohm's law: The voltage drops across parallel resistors are always equal. It should also be remembered that, when the voltage is held constant and the resistance of any resistor in a seriesparallel circuit is increased, the total current will decrease. This should not be confused as adding another parallel resistor to a parallel combination, which could reduce total resistance and increase total current flow. 
