Page 95 - Teach Yourself Electricity and Electronics

Resistances in series-parallel 75

4-9 Five resistors in parallel, R1 through R5, give a total
resistance R. See Problems 4-15 and 4-16.

When you have resistances in parallel and their values are all equal, the total resis-
tance is equal to the resistance of any one component, divided by the number of com-
ponents.

Problem 4-16
Suppose there are five resistors R1 through R5 in parallel, as shown in Fig. 4-9, all hav-
ing a value of 4.7K . What is the total resistance, R?
You can probably guess that the total is a little less than 1K or 1000 . So you can
convert the value of the single resistor to 4,700 and divide by 5, getting a total resis-
tance of 940 . This is accurate to two significant figures, the 9 and the 4; engineers
won’t usually be worried about the semantics, and you can just say “940 .”

Division of power

When combinations of resistances are hooked up to a source of voltage, they will draw
current. You can easily figure out how much current they will take by calculating the to-
tal resistance of the combination and then considering the network as a single resistor.
If the resistances in the network all have the same ohmic value, the power from the
source will be evenly distributed among the resistances, whether they are hooked up in
series or in parallel. If there are eight identical resistors in series with a battery, the net-
1
work will consume a certain amount of power, each resistor bearing /8 of the load. If you
rearrange the circuit so that the resistors are in parallel, the circuit will dissipate a cer-
tain amount of power (a lot more than when the resistors were in series), but again,
1
each resistor will handle /8of the total power load.
If the resistances in the network do not all have identical ohmic values, they divide
up the power unevenly. Situations like this are discussed in the next chapter.

Resistances in series-parallel

Sets of resistors, all having identical ohmic values, can be connected together in paral-
lel sets of series networks, or in series sets of parallel networks. By doing this, the total
power handling capacity of the resistance can be greatly increased over that of a single
resistor.