6:47 PM Ooo AT&T; LTE 89% session masteringphysics.com Problem 23.47 MasteringPh

Question

6:47 PM Ooo AT&T; LTE 89% session masteringphysics.com Problem 23.47 MasteringPhysics Problem 23.47 A cell membrane has a resistance and a capacitance and thus a characteristic time constant. Part A What is the time constant of a 8.7nm -thick membrane surrounding a 4.2x10-2mm -diameter spherical cell? Assume the resistivity of the cell membrane as 100 2 m and the dielectric constant is approximately 9.0. Express your answer to two significant figures and include the appropriate units. Value Units Submit Give Up Continue

Explanation / Answer

Given that

The thickness of the membrane is (d) =8.7nm =8.7*10-9m

The diameter of the spherical shell is (D) =4.2*10-2mm

The radius r =2.1*10-2mm then area of the spherical shell becomes (A) =pir2 =3.14*(2.1*10-2)2 =13.84*10-4mm2= 13.84*10-10m2

The resistivity of the cell membrane is (p) = 3.6*106ohm-m

The dielectric constant (k) =9

Now the capacitance of the capacitor is given by

C =keoA/d =9*8.85*10-12*13.84*10-10/8.7*10-9m=1102.356*10-13F=0.1102nF

Now resistance is given by

p =RA/L

Consider the length to be 1m then R =pL/A =(3.6*106)*1/(13.84*10-10)=2.6*103ohms

Now the time constant is given by

T =RC =(2.6*103)(0.1102*10-9) =0.2865microseconds

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