The capacitance of an object is typically explained as a measure of how much cha

Question

The capacitance of an object is typically explained as a measure of how much charge separation will be produced on the object when we apply a voltage difference to it. The equation defining the capacitance is Q = CAl/ where Q is the charge separation (+Q and -Q at two different "plates" on the capacitor), C is the capacitance, and Al/ is the potential difference. But you can also read this equation from right to left: The capacitance also identifies how much voltage difference arises across the object as a result of a particular charge separation Q. The unit we use for the capacitance is the Farad = 1 Coulomb/Volt. What is the dimensionality of the unit Farad (in terms of M, L, T, and Q -mass, length, time, and charge)? Express the unit Farad in terms of basic SI units (kilogram, meter, second, Coulomb). A typical cell membrane in an animal maintains a potential difference across the membrane of Al/ = 70 mV and the membrane has a thickness of about 8 nm.

Explanation / Answer

A) so we know PE = Q V

so volt = Joule/coloumb

but joule = N m = kg m^2/s^2

so farad = Coloumb/joule/coloumb = coloumb^2 s^2/kg m^2

B) E = V/d = 70.0E-3/8.0E-9=8.75E6

Q = C V = e0 A V/d

Q/A = e0 V/d = 8.85E-12*8.75E6= 7.74E-5

C) E doesnt change
E = 8.75E6

but now Q = k e0 A V/d

so Q/A = 3*7.74e-5= 2.32E-4 C/m^2

d) energy = q dV = 1.6E-19*70.0E-3=1.12E-20 J/ion

or 70.0E-3 eV

or 1.12E20*6.022E23 J/mol =6745 J/mol = 1.61 kcal/mol

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