In an experiment to measure the membrane potential of a living plant cell micro-electrodes are placed inside and outside the cell. The membrane potential is measured to be 120 mV and a current of 1.5 nA flows through the membrane .Assume that the current density in the cell is uniform.
The total area of the cell membrane is `2.0 m m^(2)` and its thickness is 12 `mum `.
(a) What is the current density in the membrane?
(b) What is the resistivity of the membrane ?

Explanation

(a) `j =(1)/(A) = ( 1.5 xx 10 ^(-3)A)/( 2.0 xx ( 10^(-3)m)^(2)) = 0.75 mA m^(-2)`
(b) ` E = (V)/(d) ` and `rho = ( E )/(j)`
so , `rho = (V )/ ( dj ) = ((0.120 V))/(( 12 xx 10^(-6) m ) xx ( 0. 75 xx 10^(-3)Am^(-2)))= 13 M Omega m `