Will upvote! system are given below:i(t)i₁(t)Ri(t) = i(t) + i2(t)i₂(t) = dv(t)dtdi₁(t)v(t) = i₁(t)R + L dtAssume zero initial conditions, i.e., i₁(0) = 0 and v(0) = 0.Show that the input-output plant transfer function is:K(s)i₂(t)Problem 3Consider now the same circuit, but now with known values of the circuit compo-nents (seeing your cousin's excitement, you helped them build a new one with known values!),C = 1, L = 1, R = 1s+1s² + s +1C v(t)

Given Data:An RLC circuit with the system of equations as,Supply current, Capacitor voltage,…

Answered: system are given below: i(t) i₁(t)/…

Introductory Circuit Analysis (13th Edition)

13th Edition

ISBN:9780133923605

Author:Robert L. Boylestad

Publisher:Robert L. Boylestad

Chapter1: Introduction

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system are given below:
i(t)
i₁(t)
R
i(t) = i(t) + i2(t)
i₂(t) = dv(t)
dt
di₁(t)
v(t) = i₁(t)R + L dt
Assume zero initial conditions, i.e., i₁(0) = 0 and v(0) = 0.
Show that the input-output plant transfer function is:
K(s)
i₂(t)
Problem 3
Consider now the same circuit, but now with known values of the circuit compo-
nents (seeing your cousin's excitement, you helped them build a new one with known values!),
C = 1, L = 1, R = 1
s+1
s² + s +1
C v(t)

Expert Solution

Step 1: Summarize the details given:

Given Data:

An RLC circuit with the system of equations as,

Supply current, $i open parentheses t close parentheses equals i subscript 1 open parentheses t close parentheses plus i subscript 2 open parentheses t close parentheses space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space...... open parentheses 1 close parentheses$
Capacitor voltage, $v open parentheses t close parentheses equals i subscript 1 open parentheses t close parentheses R plus L fraction numerator d i subscript 1 open parentheses t close parentheses over denominator d t end fraction space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space...... open parentheses 2 close parentheses$ and
Capacitor current, $i subscript 2 open parentheses t close parentheses equals C fraction numerator d v open parentheses t close parentheses over denominator d t end fraction space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space...... open parentheses 3 close parentheses$

To Find:

Proving the transfer function when $R equals 1 space text Ω end text comma space L equals 1 space text H end text comma space C equals 1 space text F end text$ is $K open parentheses s close parentheses equals fraction numerator s plus 1 over denominator s squared plus s plus 1 end fraction$ .

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