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E
2
R
E
R
P
E
I
2
R
P
R
I E
PI
ER
E
I
P R
P
I
E
2
P
P
I
2
I R
FIGURE 11.25
Ohm's law circle—summary of the basic formulas.
Solution:
Because the resistance (
R
) and voltage (
E
) are known, use Equation 11.24 to find
P
:
2
2
E
R
450
30 000
(
)
202 500
30 000
,
P
== =
=
6.75 W
,
,
In this section,
P
was expressed in terms of various pairs of the other three basic quantities
E
,
I
, and
R
. In practice, we should be able to express any one of the three basic quantities, as well as
P
, in terms of any two of the others. Figure 11.25 is a summary of the 12 basic formulas we should
know. The four quantities
E
,
I
,
R
, and
P
are at the center of the figure. Adjacent to each quantity are
three segments. Note that in each segment the basic quantity is expressed in terms of two other basic
quantities, and no two segments are alike.
11.7.5 e
leCtriCal
e
nergy
(K
iloWatt
-h
ours
)
Energy
(the mechanical definition) is defined as the ability to do work (energy and time are essen-
tially the same and are expressed in identical units). Energy is expended when work is done,
because it takes energy to maintain a force when that force acts through a distance. The total energy
expended to do a certain amount of work is equal to the working force multiplied by the distance
through which the force moves to do the work. In electricity, total energy expended is equal to the
rate
at which work is done, multiplied by the length of time the rate is measured. Essentially, energy
(
W
) is equal to power (
P
) times time (
t
).
The kilowatt-hour (kWh) is a unit commonly used for large amounts of electric energy or work.
The amount of kilowatt-hours is calculated as the product of the power in kilowatts (kW) and the
time in hours (hr) during which the power is used:
kWh = kW × h r
(11.25)
■
EXAMPLE 11.25
Problem:
How much energy is delivered in 4 hours by a generator supplying 12 kW?
Solution:
kWh = kW × hr = 12 × 4 = 48 kWh
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