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## Electrode Resistance

Date: March 27, 2010

The following equation can be used to estimate the resistance of a finite length ET-DSP™ electrode if you know the soil properties. The infinite length electrode approximation is not well suited for electrodes that are in the 5 to 10 m in length range; use this equation!

We usually obtain the electrical conductivity of the soil from laboratory tests. What is really cool about this equation is that all of the input data is readily available ~ and it is surprisingly accurate. I use it for both the oil and environmental applications of ET-DSP™.

The latex code used to generate the equation is:

\begin{equation}

R_e = \frac{1}

{{2{\kern 1pt} \pi {\kern 1pt} \sigma _s {\kern 1pt} h_e }}\left[ {\frac{{r_w }}

{{h_e }} + \sinh ^{ - 1} \left( {\frac{{h_e }}

{{r_w }}} \right) - \sqrt {1 + \left( {\frac{{r_w }}

{{h_e }}} \right)^2 } } \right]

\label{eqn:ElectrodeResistance01}

\end{equation}