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BME201_2010_HWK2 - NAME 125:201 INTRODUCTION TO BIOMEDICAL...

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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 ( .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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