road may still offer some resistance to the
flow of automobiles.
One could say that these roads are
parallel to each other; that the bridge on
road A is parallel to the bridge on road B.
This same example can be applied to an
electrical circuit. This example will help the
beginning student in electricity to under-
stand that in a parallel circuit the resistance
decreases because more paths are provided
for the flow of electricity.
Equal Resistors in Parallel
In Figure 7-2, the highways have been
replaced by an electrical circuit. R1
and R2
are the bridges (resistance). The auto-
mobiles are replaced by electrons flowing
along their highways, which are called
conductors. At point X, the electrons
divide, part taking road A and the other
part taking road B. At point Y, the electrons
rejoin and continue on their way. Thus, a
parallel circuit has more than one path for
current to flow. The parallel combination of
resistance units offers less resistance to
current than either single resistor.
In Figure 7-3, assume that R1
equals
100 Ω and R2
also equals 100 Ω. By com-
bining the two in a parallel circuit, the total
resistance of the circuit is only 50 Ω. The
formula for finding the total resistance of a
circuit
(RT) when the resistors are in
parallel and all of the same value is:
RT =
where RT is the total resistance, R is the
value of any one resistor and N is the num-
ber of resistors in parallel.
Apply this formula to Figure 7-3,
RT
= = 50 Ω
Like all circuits, there is a voltage, E,
across the input terminals. This potential
difference (voltage) causes the electrons to
flow in the circuit.
Let’s draw some conclusions about this
circuit.
1. The voltage across all branches or
paths of a parallel circuit is the same.
In this case, it is the same as the
applied voltage (E). You can see that
the voltage across R1
is the same as the
voltage across R2
since the ends of the
resistors are connected to the common
points X and Y that in turn are connect-
ed directly to the power source:
ET
= ER1 = ER2
100 Ω
2
R
N
56
Electricity
Road A
Road B
X
R2
Y
R1
Figure 7-2.
These two resistors are in parallel.
R2 = 100 Ω
RT = 50 Ω
Y X
R1 = 100 Ω
E
Figure 7-3.
Equal resistances in parallel.
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