5.1 SERIES CIRCUITS
The term ‘in series’ means that two or more circuits are
supplied one after the other in any single circuit, as shown diagrammatically
in Figure 5.1.
Figure 5.1 SERIES RESISTANCES
Since there is only one single path from
the power source through the circuits and back again, the same current flows
through all. The voltage, or ‘pressure’,
is reduced by resistance according to Ohm’s Law: each circuit element causes a
‘voltage drop’ across it, very similar to the ‘loss of head’ due to fluid flow
in a hydraulic system. Also the sum of
the individual volt-drops is equal to the applied voltage.
By Ohm’s Law the volt-drop V1 across the load R1 is
V1
=I x R1
and similarly V2 = I x R2, I being the same for each of the cases.
Therefore: V1 + V2 + …. = IR1 + IR2 + ….
=
I(R1 + R2 + .… )
But the sum of the
individual volt-drops V1 +
V2 + …. = V (the applied voltage).
By Ohm’s Law for the
equivalent circuit V = IR.
Hence:
IR =I(R1+R2+ ....)
or R =R1+R2+ ....
That is to say, the total resistance of a series circuit is equal to the
sum of all the individual resistances.
It is evident that the failure of
any single component in a series circuit interrupts the supply to all; also
that each element of load must work at a reduced voltage. For these reasons the series arrangement of
loads is seldom used in power circuits.
5.2 PARALLEL CIRCUITS
The term ‘in parallel’ means that the circuits are so
arranged that there is a separate path through each, as shown in Figure 5.2.
Figure 5.2 PARALLEL RESISTANCES
The voltage applied to every circuit element is the same
throughout. The total current divides
between the circuits according to the resistance of each element, so that the
current flowing through each individual circuit is less than the total, and the
sum of the currents flowing through the individual elements is equal to the
total available current.
By Ohm’s Law the current I1 flowing through the load R1 is:
I1
|
=
|
V
|
R1
|
.
and
similarly
and
similarly
I2
|
=
|
V
|
R2
|
But the sum of the currents flowing in each
individual circuit
I1
|
+
|
I2
|
+
|
….
|
=
|
I
(the total current)
|
Hence:
I
|
=
|
V (
|
1
|
+
|
1
|
+
|
….)
|
R1
|
R2
|
or
|
 I |
=
|
1
|
+
|
1
|
+
|
….
|
V
|
R1
|
R2
|
But by Ohm’s Law for the equivalent circuit V
|
=
|
IR
|
or
|
 I |
=
|
1
|
V
|
R
|
\
|
1
|
=
|
1
|
+
|
1
|
+
|
….
|
R
|
R1
|
R2
|
That is to say, the inverse of the equivalent resistance
of a set of parallel circuits is equal to the sum of the inverses of each
individual resistance.
It is evident that for the power engineer the parallel
circuit has two important practical advantages.
First, the failure of any element of load has no effect on the rest;
they continue to receive a supply at the correct voltage and to draw the
current which each individually requires.
Second, all apparatus is supplied at the same voltage. Consequently, the parallel circuit is used
almost exclusively for power supply in industrial plant.
It should be observed in passing that the characteristic
of the series circuit, in which resistances in series have the effect of
reducing the voltage at different points of the circuit, finds wide practical
application in electronic apparatus such as radio, control, and ‘solid-state’
measuring equipment.
5.3 SUMMARY
If R is the single resistance equivalent to a number of individual
resistances R1, R2,
R3, …, then:
(a)
if R1, R2 etc.
are in series,
R = R1 + R2 + R3 +
.…
(b)
if R1, R2 etc.
are in parallel,
1
|
=
|
1
|
+
|
1
|
+
|
1
|
+
|
….
|
R
|
R1
|
R2
|
R3
|
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