An individual cell such as an egg cell $($an ovum, produced in the ovaries$)$ is commonly organized spatially, as manifested in part by asymmetries in the cell membrane. These asymmetries include non$-$uniform distributions of ion transport mechanisms, which result in a net electric current entering one region of the membrane and leaving another. These steady cellular currents may regulate cell polarity, leading $($in the case of eggs$)$ to embryonic polarity; therefore, scientists are interested in measuring them.

These cellular currents move in loops through extracellular fluid. Ohm's law requires that there be a voltage difference between any two points in this current$-$carrying fluid surrounding cells. Although the currents may be significant, the extracellular voltage differences are tiny$-$on the order of nanovolts. If we can map the voltage differences in the fluid outside a cell, we can calculate the current density by using Ohm's law, assuming that the resistivity of the fluid is known. We cannot measure these voltage differences by spacing two electrodes $10$ or $20m$ apart because the dc impedance $($the resistance$)$ of such electrodes is high and the inherent noise in signals detected at the electrodes far exceeds the cellular voltages.

One successful method of measurement uses an electrode with a ball$-$shaped end made of platinum that is moved sinusoidally between two points in the fluid outside a cell. The electric potential that the electrode measures, with respect to a distant reference electrode, also varies sinusoidally$.$ The dc potential difference between the two extremes $($the two points in the fluid$)$ is then converted to a sine$-$wave ac potential difference. The platinum electrode behaves as a capacitor in series with the resistance of the extracellular fluid. This resistance, called the access resistance $(R_A),$ has a value of about $\frac{}{10}a,$ where $$ is the resistivity of the fluid $($usually expressed in $*cm)$ and $a$ is the radius of the ball electrode. The platinum ball typically has a diameter of $20m$ and a capacitance of $10$ nF ; the resistivity of many biological fluids is $100$

Part A

The signal from the oscillating electrode is fed into an amplifier, which reports the measured voltage as an rms value, $30$ nV $.$ What is the potential difference between the two extremes?

$8\mathrm{.}5$ nV

$4\mathrm{.}2$ nV

$3\mathrm{.}0$ nV

$6\mathrm{.}0$ nV

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