A capacitor stores a separation of charge. To separate the charges on a capacitor, you have to move charges against where the E field wants to push them (the oppositely charges on the two plates are attracted and want to move together), so charging takes work. That work becomes stored energy -- just like carrying water up a hill so that you can let it roll down at a later time and turn a generator. The total amount of energy stored in a capacitor is ½|Q||ΔV|. We'll use this to determine the amount of energy stored in a cell membrane.In discussion, we found that a cell membrane maintains a potential difference of about 70 mV (0.07 V) between the inside and outside of the membrane. We also found that a 1 μm by 1 μm section of the membrane has a capacitance of about 1.75  10-15 F.The radius of the cell is 10 μm. 4. What is the total energy stored in the full cell membrane?The answer is NOT 1.539e-13, 8.56e-18, or 4.28e-18.

Question
Asked Oct 14, 2019

A capacitor stores a separation of charge. To separate the charges on a capacitor, you have to move charges against where the E field wants to push them (the oppositely charges on the two plates are attracted and want to move together), so charging takes work. That work becomes stored energy -- just like carrying water up a hill so that you can let it roll down at a later time and turn a generator. The total amount of energy stored in a capacitor is ½|Q||ΔV|. We'll use this to determine the amount of energy stored in a cell membrane.

In discussion, we found that a cell membrane maintains a potential difference of about 70 mV (0.07 V) between the inside and outside of the membrane. We also found that a 1 μm by 1 μm section of the membrane has a capacitance of about 1.75  10-15 F.

The radius of the cell is 10 μm. 

4. What is the total energy stored in the full cell membrane?

The answer is NOT 1.539e-13, 8.56e-18, or 4.28e-18. 

check_circleExpert Solution
Step 1

The equation for the capacitance is given by

E0.4
C =
(1)
d
Here, C is the capacitance, E is the absolute permittivity, A is the area of the plates and d is the
distance between the plates.
Rewrite the above equation for d.
d =
C
The value of 5 is 8.854x102 F/m . Substitute the numerical values in the above equation to find the
distance between the inside and the outside of the membrane.
(8.854 x1012 F/m)(1x10
d
m)
1.75x1015 F
= 5.06 x 10 m
The equation for the total area of the cell membrane is
A = r2
Here, r is the radius of the cell
Put the above equation in equation (1)
C =
d
(2)
help_outline

Image Transcriptionclose

E0.4 C = (1) d Here, C is the capacitance, E is the absolute permittivity, A is the area of the plates and d is the distance between the plates. Rewrite the above equation for d. d = C The value of 5 is 8.854x102 F/m . Substitute the numerical values in the above equation to find the distance between the inside and the outside of the membrane. (8.854 x1012 F/m)(1x10 d m) 1.75x1015 F = 5.06 x 10 m The equation for the total area of the cell membrane is A = r2 Here, r is the radius of the cell Put the above equation in equation (1) C = d (2)

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Step 2

The equation for the charge store...

Q CAV
Here, Q is the charge stored.
Put equation (2) in the above equation.
AV
d
Thus, the equation for the total energy stored is
UOAV
- AV Δν
2 d
1 57(AV
2 d
Substitute the numerical values in the above equation
8.854 x1012 F/m) (10 x10" m) (0.07 V)
1 (
U
2
(5.06x10 m
=1.35x1015 J
help_outline

Image Transcriptionclose

Q CAV Here, Q is the charge stored. Put equation (2) in the above equation. AV d Thus, the equation for the total energy stored is UOAV - AV Δν 2 d 1 57(AV 2 d Substitute the numerical values in the above equation 8.854 x1012 F/m) (10 x10" m) (0.07 V) 1 ( U 2 (5.06x10 m =1.35x1015 J

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