e x a m p l e 2.33 v o l t a g e - c o n t r o l l e d r e s i s t o r Thus far
we have dealt with resistors that have a fixed resistance. However, like dependent
sources, we can also have resistors whose values depend on other parameters. As an
example, Figure 2.71 depicts a voltage-controlled resistor whose resistance RX is a
function of vI .
Let us suppose we are interested in determining vO as a function of vI for
RX = f (vI ) = Ro vI
where Ro is some known constant. Let Ro = 5 k/V.
First, R1 and R2 form a simple voltage divider, and since R1 = R2 , we have vI = V/2.
Second, RL and RX also form a voltage divider. Therefore,
vO = V
=V
=V
=V
=V
=
RX
RL + RX
Ro vI
RL + Ro vI
5 k/vI
10 k + 5 k/vI
vI
2 + vI
V
2
2+
V2
4+V
V
2
.
Substituting V = 5 V, we find that vO = 25/9 V.
R1 = 100 k Ω
F I G U R E 2.71 Circuit with
voltage-dependent resistor.
V
+
5 V
-
vI
R2 = 100 k Ω
107a
RL = 10 kΩ
vO
RX = f(vI)