NAME:_______________________________
1
125:201 INTRODUCTION TO BIOMEDICAL ENGINEERING, Fall 2010
Bioelectrical Phenomena
Instructor:
Nada Boustany
HOMEWORK #2- Due THURSDAY
Dec. 2
Problem 1:
Relationships, variables and constants:
σ
: conductivity in (
Ω
.m)
-1
= |z|.F.u.c
Einstein relationship: D/u= (RT)/(|z| F)
E= -d
φ
/dx
J=
Γ
.z.F
z = valence of the ion.
c = concentration in moles/cm
3
u = mobility in cm
2
/volt/s
D = diffusivity in cm
2
/s
F is Faraday’s constant= 96,500 C/mole
R is the gas constant = 8.31 J/mole/K
T is the temperature in Kelvin (K).
J is the current density in C/cm
2
/s
φ
is the electrical potential in Volts
Γ
is the molecular flux in moles/cm
2
/s
ρ
is the charge density in Coul/cm
3
A cell has a membrane, which is permeable only to K
+
.
The concentrations of K+ are 5mM outside and 145mM inside.
a.
Using Ohm’s law, J
drift
=
σ
E, rewrite the electrical drift current, J
drift
, for
K+ as
a function of mobility, concentration, the electric potential and x.
b.
Using Fick’s law,
Γ
diff
= -D.dc/dx, derive the diffusion current, J
diff
, for K+ as a
function of diffusivity, concentration and x.
c.
Assuming that K+ ions are at equilibrium, write an expression relating J
drift
to
J
diff
.
d.
Integrate the equation found in Part c and derive an expression for the Nernst
potential for K+.

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