Biomedical Engineering Reference
In-Depth Information
p = vi
p =
−
vi
i
1
1
+
v
−
+
v
−
Circuit
Element
Circuit
Element
2
2
(a)
(b)
p =
−
vi
p i
=
i
1
1
−
+
−
+
Circuit
Element
Circuit
Element
2
2
i
(c)
(d)
FIGURE 9.9
Polarity references for four cases of current and voltage. Cases (a) and (d) result in positive power
being consumed by the circuit element. Cases (b) and (c) result in negative power being extracted from the circuit
element.
where
is energy measured in joules (J). Power is
usually determined by the product of voltage across a circuit element and the current
through it. By convention, we assume that a positive value for power indicates that power
is being delivered (or absorbed or consumed) by the circuit element. A negative value for
power indicates that power is being extracted or generated by the circuit element—that
is, a battery.
Figure 9.9 illustrates the four possible cases for a circuit element's current and voltage
configuration. According to convention, if both
p
is power measured in watts (W), and
w
are positive, with the arrow and
polarity shown in Figure 9.9(a), energy is absorbed (either lost by heat or stored). If either
the current arrow or voltage polarity is reversed, as in (b) and (c), energy is supplied to the
circuit. Note that if both the current direction and voltage polarity are reversed together,
as in (d), energy is absorbed.
A passive circuit element is defined as an element whose power is always positive or
zero, which may be dissipated as heat (resistance), stored in an electric field (capacitor),
or stored in a magnetic field (inductor). We define an active circuit element as one whose
power is negative and capable of generating energy. Energy is given by
i
and
v
Z
t
w
ð
t
Þ¼
pdt
ð
9
:
7
Þ
1
9.3.5 Sources
Sources are two terminal devices that provide energy to a circuit. There is no direct
voltage-current relationship for a source; when one of the two variables is given, the other
