Versine

Figure 1
Figure 1

Relationship

\[ R = \frac{C^{2}}{8V} \]

Derivation

Consider \(\triangle aox\).

\[\begin{align} R^{2} & = \bigg( \frac{C}{2} \bigg)^{2} + (R-V)^{2} \\ R^{2} & = \frac{C^{2}}{4} + R^{2} + V^{2} - 2RV \\ 2RV & = \frac{C^{2}}{4} + V^{2} \\ R & = \frac{C^{2}}{8V} + \frac{V}{2} \end{align}\]

where \(C \gg V\)

\[ R = \frac{C^{2}}{8V} \]