Environmental Engineering Reference
In-Depth Information
Using power of tens,
E
R
2
= (4 × 10
-3
) × (40 × 10
3
) = 4.0 × 40 = 160 volts
Therefore,
E
b
= 160 volts
C
urrent
in
p
arallel
C
irCuits
In a series circuit, a single current flows. Its value is determined in part by the total
resistance of the circuit; however, the source current in a parallel circuit divides
among the available paths in relation to the value of the resistors in the circuit. O h m's
law remains unchanged. For a given voltage, current varies inversely with resistance.
Note:
Ohm's law states that the
current in a circuit is inversely proportional to the
circuit resistance
. This fact, important as a basic building block of electrical theory,
is also important in the following explanation of current flow in parallel circuits.
The behavior of current in a parallel circuit is best illustrated by example (see
Figure 10.21). The resistors
R
1
,
R
2
, and
R
3
are in parallel with each other and with the
battery. Each parallel path is then a branch with its own individual current. When the
total current (
I
T
) leaves the voltage source (
E
), part
I
1
of current
I
T
will flow through
R
1
, part
I
2
will flow through
R
2
, and
I
3
through
R
3
. The branch currents
I
1
,
I
2
, and
I
3
can be different; however, if a voltmeter (used for measuring the voltage of a circuit)
is connected across
R
1
,
R
2
, and
R
3
, then the respective voltages
E
1
,
E
2
, and
E
3
will be
equal. Therefore,
E
=
E
1
=
E
2
=
E
3
(10.12)
The total current,
I
T
, is equal to the sum of all branch currents:
I
T
=
I
1
+
I
2
+
I
3
(10.13)
This formula applies for any number of parallel branches, whether the resistances
are equal or unequal.
I
T
I
1
I
2
I
3
+
E
1
E
2
E
3
R
1
R
2
R
3
E
-
FIGURE 10.21
Parallel circuit.
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