Kirchhoff’s voltage law is still true.
That is to say, since all components are
connected in parallel, there is only one
voltage drop. That one voltage drop is
equal to the source or applied voltage.
2. The total current in the circuit is equal
to the sum of all the currents flowing in
the branches of the parallel circuit or:
IT
= IR1 + IR2
An example using actual values will
help you understand this.
In Figure 7-4, total resistance
(RT) of
the circuit can be found using:
RT
= = = 100 Ω
The current flowing in the circuit can
be found by Ohm’s law.
I = = = 2 A
When the current of 2 amperes reaches
point X, it divides. One ampere flows
around branch A through
R1, and one
ampere flows around branch B through
R2.
At point Y, the two currents rejoin.
The total current IT = 2 amps
Current in branch A = 1 amp
Current in branch B = 1 amp
IT = 1 amp + 1 amp = 2 amps
Again, note that Kirchhoff’s other law,
Kirchhoff’s current law, still holds true. All
current that flows into a junction will flow
out of it.
Unequal Resistors in
Parallel
So far we have assumed that R1 equals
R2. This is not always so. Often they are
unequal, and there is not an equal division
of currents flowing in the branches of the
parallel circuit.
In Figure 7-5, when the current reaches
point X, it will still divide, but the greater
amount of current will flow through the
branch B, because branch B has less resis-
tance than branch A.
Computing the total resistance of a
parallel circuit having two unequal resis-
tors is not too difficult. The following
formula is called the product over the sum
method due to the arithmetic operations
involved. It can be used for any two
resistors in parallel.
200 V
100 Ω
E
R
200 Ω
2
R
N
Chapter 7 Parallel Circuits
57
R1 = 200 Ω
IR1 = 1 A
ET = 200 V
I
T
= 2 A
Branch
A
R2 = 200 Ω
IR2 = 1 A
Branch
B
IT = 2 A
X
Y
Figure 7-4.
The circuit current divides between the
branches of the parallel circuit. Kirchhoff’s
current law still holds true!
R1 = 100 Ω
ET = 200 V
Branch
A
R2 = 50 Ω
Branch
B
X
Y
Figure 7-5.
Unequal resistances in parallel.