An RC circuit
Figure 3.33: An RC circuit and the associated signal-flow diagram.
We can model electrical circuits using streams to represent the values of currents or voltages at a sequence of times. For instance, suppose we have an
RC
circuit consisting of a resistor of resistance
R
and a capacitor of capacitance
C
in series. The voltage response
v
of the circuit to an injected current
i
is determined by the formula in figure 3.33, whose structure is shown by the accompanying signal-flow diagram.
Write a procedure
RC
that models this circuit.
RC
should take as inputs the values of
R
,
C
, and
dt
and should return a procedure that takes as inputs a stream representing the current
i
and an initial value for the capacitor voltage
v₀
and produces as output the stream of voltages
v
. For example, you should be able to use
RC
to model an
RC
circuit with
R = 5
ohms,
C = 1
farad, and a
0.5
-second time step by evaluating
(define RC1 (RC 5 1 0.5))
. This defines
RC1
as a procedure that takes a stream representing the time sequence of currents and an initial capacitor voltage and produces the output stream of voltages.