The potential difference across a cell membrane from outside...

The potential difference across a cell membrane from outside to inside is initially at $-90 \mathrm{mV}$ (when in its resting phase). When a stimulus is applied, $\mathrm{Na}^{+}$ ions are allowed to move into the cell such that the potential changes to $+20 \mathrm{mV}$ for a short interval of time. (a) If the membrane capacitance per unit area is $1 \mu \mathrm{F} / \mathrm{cm}^{2}$ how much charge moves through a membrane of area $0.05 \mathrm{cm}^{2} ?$ (b) The charge on $\mathrm{Na}^{+}$ is te. How many ions move through the membrane?

The potential difference across a cell membrane from outside to inside is initially at $-90 \mathrm{mV}$ (when in its resting phase). When a stimulus is applied, $\mathrm{Na}^{+}$ ions are allowed to move into the cell such that the potential changes to $+20 \mathrm{mV}$ for a short interval of time.
(a) If the membrane capacitance per unit area is $1 \mu \mathrm{F} / \mathrm{cm}^{2}$ how much charge moves through a membrane of area $0.05 \mathrm{cm}^{2} ?$
(b) The charge on $\mathrm{Na}^{+}$ is te. How many ions move through the membrane?

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Key Concepts

Electric Potential Difference

Electric potential difference, or voltage, across a membrane is the difference in electric potential between the inside and outside of the cell. This voltage difference is essential for driving the movement of ions, which underlies many cellular processes including the generation of action potentials.

Charge Calculation Using Q = CV

The relationship Q = CV, where Q is the charge, C is the capacitance, and V is the voltage, is fundamental for calculating the amount of charge transferred when there is a change in membrane potential. This concept is vital in understanding how electrical signals are generated and propagated in cells.

Membrane Capacitance

Membrane capacitance is a measure of a cell membrane’s ability to store electrical charge per unit area. In biological systems, the lipid bilayer of the membrane acts as a capacitor, with the stored charge being critical for maintaining and propagating electrical signals, such as in nerve and muscle cells.

Elementary Charge

The elementary charge is the magnitude of the charge carried by a single ion, such as Na?. It provides the basis for converting a total charge in coulombs into the number of ions involved in an electrical event, linking macroscopic electrical measurements to the molecular scale.

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