2) Lung mechanics relate gas flow (V measured in L s¹) to pressure at the airway opening (P measured in cmH₂O), in much the same way that electrical impedance relates current to voltage. A simple model of the lungs is a series RLC circuit, describing the resistance of the airways (R, in cmH₂O L¹ s), inertia of the gas (L, in cmH₂O L¹¹ s²), and compliance of the lung (C, in L cmH₂0¹¹). a) Write the Laplace-domain total impedance Z(s) of the series RLC circuit. Note that impedance is the transfer function between pressure P(s) and flow V(s). b) Write the frequency response Z(jw) of the series RLC circuit in terms of real and imaginary components (i.e., a and b in [a + jb]). c) Derive an expression for the magnitude of the impedance [Z(jw)| in terms of w, R, L, and C. What is I|Z(jw) in the limit as w→ 0? What is |Z(jw) in the limit as w→ ∞ ?
2) Lung mechanics relate gas flow (V measured in L s¹) to pressure at the airway opening (P measured in cmH₂O), in much the same way that electrical impedance relates current to voltage. A simple model of the lungs is a series RLC circuit, describing the resistance of the airways (R, in cmH₂O L¹ s), inertia of the gas (L, in cmH₂O L¹¹ s²), and compliance of the lung (C, in L cmH₂0¹¹). a) Write the Laplace-domain total impedance Z(s) of the series RLC circuit. Note that impedance is the transfer function between pressure P(s) and flow V(s). b) Write the frequency response Z(jw) of the series RLC circuit in terms of real and imaginary components (i.e., a and b in [a + jb]). c) Derive an expression for the magnitude of the impedance [Z(jw)| in terms of w, R, L, and C. What is I|Z(jw) in the limit as w→ 0? What is |Z(jw) in the limit as w→ ∞ ?
Introductory Circuit Analysis (13th Edition)
13th Edition
ISBN:9780133923605
Author:Robert L. Boylestad
Publisher:Robert L. Boylestad
Chapter1: Introduction
Section: Chapter Questions
Problem 1P: Visit your local library (at school or home) and describe the extent to which it provides literature...
Related questions
Question
![2) Lung mechanics relate gas flow (V measured in L s¹) to pressure at the airway opening (P
measured in cmH₂O), in much the same way that electrical impedance relates current to
voltage. A simple model of the lungs is a series RLC circuit, describing the resistance of the
airways (R, in cmH₂O L´¹ s), inertia of the gas (L, in cmH₂O L´¹ s²), and compliance of the
lung (C, in L cmH₂0¹¹).
a) Write the Laplace-domain total impedance Z(s) of the series RLC circuit. Note that
impedance is the transfer function between pressure P(s) and flow V(s).
b)
Write the frequency response Z(jw) of the series RLC circuit in terms of real and
imaginary components (i.e., a and b in [a + jb]).
c) Derive an expression for the magnitude of the impedance [Z(jw)| in terms of w, R, L,
and C. What is IZ(jw) in the limit as w → 0 ? What is |Z (jw) in the limit as w→ ∞0 ?
IN](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Ff615326e-a737-4ff6-ab97-e2ce7686d995%2Fc7093e3b-9099-4a84-8c08-fa18a5cb43c7%2Fn0r9l4i_processed.jpeg&w=3840&q=75)
Transcribed Image Text:2) Lung mechanics relate gas flow (V measured in L s¹) to pressure at the airway opening (P
measured in cmH₂O), in much the same way that electrical impedance relates current to
voltage. A simple model of the lungs is a series RLC circuit, describing the resistance of the
airways (R, in cmH₂O L´¹ s), inertia of the gas (L, in cmH₂O L´¹ s²), and compliance of the
lung (C, in L cmH₂0¹¹).
a) Write the Laplace-domain total impedance Z(s) of the series RLC circuit. Note that
impedance is the transfer function between pressure P(s) and flow V(s).
b)
Write the frequency response Z(jw) of the series RLC circuit in terms of real and
imaginary components (i.e., a and b in [a + jb]).
c) Derive an expression for the magnitude of the impedance [Z(jw)| in terms of w, R, L,
and C. What is IZ(jw) in the limit as w → 0 ? What is |Z (jw) in the limit as w→ ∞0 ?
IN
Expert Solution
Step 1
Given data
Lungs are modeled in the simple circuit.
We have to determine the Laplace-domain of , and when & .
Step by step
Solved in 5 steps with 1 images
Knowledge Booster
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, electrical-engineering and related others by exploring similar questions and additional content below.Recommended textbooks for you
Introductory Circuit Analysis (13th Edition)
Electrical Engineering
ISBN:
9780133923605
Author:
Robert L. Boylestad
Publisher:
PEARSON
Delmar's Standard Textbook Of Electricity
Electrical Engineering
ISBN:
9781337900348
Author:
Stephen L. Herman
Publisher:
Cengage Learning
Programmable Logic Controllers
Electrical Engineering
ISBN:
9780073373843
Author:
Frank D. Petruzella
Publisher:
McGraw-Hill Education
Introductory Circuit Analysis (13th Edition)
Electrical Engineering
ISBN:
9780133923605
Author:
Robert L. Boylestad
Publisher:
PEARSON
Delmar's Standard Textbook Of Electricity
Electrical Engineering
ISBN:
9781337900348
Author:
Stephen L. Herman
Publisher:
Cengage Learning
Programmable Logic Controllers
Electrical Engineering
ISBN:
9780073373843
Author:
Frank D. Petruzella
Publisher:
McGraw-Hill Education
Fundamentals of Electric Circuits
Electrical Engineering
ISBN:
9780078028229
Author:
Charles K Alexander, Matthew Sadiku
Publisher:
McGraw-Hill Education
Electric Circuits. (11th Edition)
Electrical Engineering
ISBN:
9780134746968
Author:
James W. Nilsson, Susan Riedel
Publisher:
PEARSON
Engineering Electromagnetics
Electrical Engineering
ISBN:
9780078028151
Author:
Hayt, William H. (william Hart), Jr, BUCK, John A.
Publisher:
Mcgraw-hill Education,