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A model of a red blood cell portrays the cell as a capacitor with two spherical plates. It is a positively charged conducting liquid sphere of area A , separated by an insulating membrane of thickness t from the surrounding negatively charged conducting fluid. Tiny electrodes introduced into the cell show a potential difference of 100 mV across the membrane. Take the membrane's thickness as 100 nm and its dielectric constant as 5.00. (a) Assume that a typical red blood cell has a mass of 1.00 X 10 –12 kg and density 1 100 kg/m 3 . Calculate its volume and its surface area, (b) Find the capacitance of the cell, (c) Calculate the charge on the surfaces of the membrane. How many electronic charges does this charge represent?

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Physics for Scientists and Enginee...

9th Edition
Raymond A. Serway + 1 other
Publisher: Cengage Learning
ISBN: 9781305116399

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Chapter
Section
BuyFindarrow_forward

Physics for Scientists and Enginee...

9th Edition
Raymond A. Serway + 1 other
Publisher: Cengage Learning
ISBN: 9781305116399
Chapter 26, Problem 26.61AP
Textbook Problem
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A model of a red blood cell portrays the cell as a capacitor with two spherical plates. It is a positively charged conducting liquid sphere of area A, separated by an insulating membrane of thickness t from the surrounding negatively charged conducting fluid. Tiny electrodes introduced into the cell show a potential difference of 100 mV across the membrane. Take the membrane's thickness as 100 nm and its dielectric constant as 5.00. (a) Assume that a typical red blood cell has a mass of 1.00 X 10–12 kg and density 1 100 kg/m3. Calculate its volume and its surface area, (b) Find the capacitance of the cell, (c) Calculate the charge on the surfaces of the membrane. How many electronic charges does this charge represent?

(a)

To determine

The volume and surface area of the plate.

Explanation of Solution

Given info: The density of the red blood cell is 1100kg/m3 , the mass of the blood is 1.00×1012kg , the potential difference across the membrane is 100mV , the thickness of the membrane is 100nm and the dielectric constant is 5.00 .

Formula to calculate the volume is,

V=Mρ

Here,

V is the volume of the sphere.

ρ is the density of the blood.

M is the mass of the red blood cell.

Substitute 1100kg/m3 for ρ and 1.00×1012kg for M in above equation.

V=1.00×1012kg1100kg/m3=9.09×1016m3

Thus, the volume of the sphere is 9.09×21016m3 .

Formula to calculate the volume of sphere is,

V=43πr3

Substitute 9.09×21016m3 for V in above equation to find r

(b)

To determine

The capacitance of the cell.

(c)

To determine

The number of the electronic charges.

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Chapter 26 Solutions

Physics for Scientists and Engineers, Technology Update (No access codes included)
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