Biomedical Engineering Reference
In-Depth Information
i(t)
+
v
(
t
)
−
R
+
v
(
t
)
−
R
(b)
i
(
t
)
(a)
FIGURE 9.12
An ideal resister with resistance R in ohms (
O
).
There are two ways to write Ohm's law, depending on the current direction and voltage
polarity. Ohm's law is written for Figure 9.12a as
v
¼
iR
ð
9
:
8
Þ
and for Figure 9.12b as
v
¼
iR
ð
9
:
9
Þ
In this topic, we use the convention shown in Figure 9.12a to write the voltage drop
across a resistor. As described, the voltage across a resistor is equal to the product of the
current flowing through the element and its resistance,
. This linear relationship does
not apply at very high voltages and currents. Some electrically conducting materials have
a very small range of currents and voltages in which they exhibit linear behavior. This is
true of many physiological models as well: linearity is observed only within a range of
values. Outside this range, the model is nonlinear. We define a short circuit as shown in
Figure 9.13a, with
R
R
¼
0
and having a 0 V voltage drop. We define an open circuit as shown
in Figure 9.13b, with
and having 0 A current pass through it.
Each material has a property called resistivity
R
¼1
(
r
)
that indicates the resistance of the
material. Conductivity
) is the inverse
of resistance. Conductance is measured in units called siemens (S) and has units of A/V.
In terms of conductance, Ohm's law is written as
(
s
)
is the inverse of resistivity, and conductance (
G
i
¼
Gv
ð
9
:
10
Þ
Short Circuit
Open Circuit
i =
0
A
i
+
+
R
= 0
Ω
v =
0
V
R =
v
−
−
(a)
(b)
FIGURE 9.13
Short and open circuits.
