# 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.

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