\"A cell membrane has a resistance and a capacitance and thus a characteristic t

Question

"A cell membrane has a resistance and a capacitance and thus a characteristic time constant. What is the time constant of a 8.5nm -thick membrane surrounding a 4.6×10-2 mm-diameter spherical cell? Assume the resistivity of the cell membrane as 3.6*10^6 ohm*m and the dielectric constant is approximately 9.0."

I am trying to use the equation: time constant=RC. And R=(rho)(L)/A. And C=KEA/d

I keep getting 5*10^-8s. Which is not right. I have also referenced the answers for my book and that answer is also wrong (I got 5*10^-16 and 4.6*10^-18s).

Explanation / Answer

   Area   A   =    * (diameter/2)2                         =   3.14 * (4.6 * 10-6/2)2                      =   1.66 * 10-11 m2    thickness d  =   8.5 nm   =   8.5 * 10-9    m    Resistance   R   =    * d / A                               =   3.6 * 10-6 * 8.5 * 10-9 / 1.66 * 10-11                               =   1.84 * 10-3       Capacitance   C   =   k * 0 * A / d                                  =   9.0 * 8.85 * 10-12 * 1.66 * 10-11 / 8.5 * 10-9                                  =   1.55 * 10-13   F    Time constant   t   =   R * C                                  =   1.84 * 10-3 * 1.55 * 10-13                                  =   2.85 * 10-16    s    please try this.               

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