Question

The membrane of a living cell is an insulator that separates two conducting fluids. Thus, it functions as a capacitor.
The membrane is not a perfect insulator, however. It has a small conductance, making it a leaky capacitor. In this
problem, you will estimate the RC time constant of the cell membrane.
(a) A cell membrane typically has a capacitance per unit area on the order of 1 μF/cm2 — i.e., 1 cm2 of the
membrane material would have a capacitance of 1 μF. It is believed that the membrane material is a dielectric
with κ ≈ 3. What thickness does this imply?
(b) Electric measurements indicate that the resistance of 1 cm2 of cell membrane is R ≈ 1000 Ω. What is the
resistivity ρ of the membrane material?
(c) Find an expression for the time constant τ = RC of the membrane in terms of ρ, κ, and 0. Show that it is
independent of the area of the membrane. This should be a symbolic result, not a numerical value.
(d) What is the value of the time constant of the cell membrane? If there were no active charge transport, this is
the time it would take the potential across a cell membrane to decay to about 37 percent of its initial value.

Answer 1