Capacitance — Question 9

Question 9

A one-electron transfer defines a discrete voltage step

Use $e=1.602176634\times10^{-19}$ C, exact. An ideal capacitor has C=20.0 aF, where $1\,\mathrm{aF}=10^{-18}$ F. It begins neutral. Electrons are transferred one at a time from plate A to plate B; ignore quantum corrections to the classical model.

1. Find the voltage increase VA-VB per electron transferred.

2. Find the smallest integer number of transfers that produces at least .100 V and the resulting voltage.

Question 9 - Solution

A one-electron transfer defines a discrete voltage step

(a) Method and calculation

$$\Delta q_A=+e,\quad\Delta v=e/C=8.01088317\times10^{-3}\,\mathrm V.$$$$v_N=Ne/C.$$

(b) Interpretation and further calculation

$$N_{\min}=\left\lceil\frac{C(.100\,\mathrm V)}e\right\rceil=\lceil12.4830\rceil=13.$$$$v_{13}=.104141481\,\mathrm V.$$

Physical check

Removing electrons leaves A positive; the integer constraint prevents choosing a fractional transferred electron.