A series RLC circuit

A series RLC circuit consists of a resistor, a capacitor, and an inductor connected in series, as shown in figure 3.36. If R , L , and C are the resistance, inductance, and capacitance, then the relations between voltage ( v ) and current ( i ) for the three components are described by the equations


and the circuit connections dictate the relations


Combining these equations shows that the state of the circuit (summarized by vC , the voltage across the capacitor, and iL , the current in the inductor) is described by the pair of differential equations


The signal-flow diagram representing this system of differential equations is shown in figure 3.37.


Figure 3.36: A series RLC circuit.


Figure 3.37: A signal-flow diagram for the solution to a series RLC circuit.

Write a procedure RLC that takes as arguments the parameters R , L , and C of the circuit and the time increment dt . In a manner similar to that of the RC procedure of exercise 3.73 , RLC should produce a procedure that takes the initial values of the state variables, vC₀ and iL₀ , and produces a pair (using cons ) of the streams of states vC and iL . Using RLC , generate the pair of streams that models the behavior of a series RLC circuit with K = 1 ohm, C = 0.2 farad, L = 1 henry, dt = 0.1 second, and initial values iL₀ = 0 amps and vC₀ = 10 volts.

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