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A series RLC circuit
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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.