3 Leaky Capacitor The membrane of a living cell is an insulator that separates two conducting fluids. Thus, it functions as a capacitor. The membrane is not a perfect insulator, however. It has a small conductance, making it a leaky capacitor. In this problem, you will estimate the RC time constant of the cell membrane. (a) A cell membrane typically has a capacitance per unit area on the order of 1 μF/cm²- i.e., 1 cm² of the membrane material would have a capacitance of 1 µF. It is believed that the membrane material is a dielectric with x ≈ 3. What thickness does this imply for the cell membrane? (b) Electric measurements indicate that the resistance of 1 cm² of cell membrane is R 1000. What is the resistivity p of the membrane material? (c) Find an expression for the time constant 7 = RC of the membrane in terms of p, x, and €0. Show that it is inde- pendent of the area of the membrane. This should be a symbolic result, not a numerical value.

3 Leaky Capacitor The membrane of a living cell is an insulator that separates two conducting fluids. Thus, it functions as a capacitor. The membrane is not a perfect insulator, however. It has a small conductance, making it a leaky capacitor. In this problem, you will estimate the RC time constant of the cell membrane. (a) A cell membrane typically has a capacitance per unit area on the order of 1 μF/cm²- i.e., 1 cm² of the membrane material would have a capacitance of 1 µF. It is believed that the membrane material is a dielectric with x ≈ 3. What thickness does this imply for the cell membrane? (b) Electric measurements indicate that the resistance of 1 cm² of cell membrane is R 1000. What is the resistivity p of the membrane material? (c) Find an expression for the time constant 7 = RC of the membrane in terms of p, x, and €0. Show that it is inde- pendent of the area of the membrane. This should be a symbolic result, not a numerical value.

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...

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