Question

The given figure depicts an array used in DC resistivity surveys, where the current electrodes are denoted by C1 and C2, and potential electrodes by P1 and P2. If all the electrodes are equally spaced, then the given array corresponds to which one of the following configurations? \includegraphics[width=0.5\linewidth]{5.png}

• A. Wenner
• B. Schlumberger
• C. Dipole–Dipole
• D. Pole–Pole

Hint:

If you see two adjacent electrodes labeled as the current pair and another adjacent pair as the potential pair, with a gap between the pairs, think \textbf{Dipole–Dipole}. If all four are equally spaced but the potential pair is in the middle, that's \textbf{Wenner}.

Answer 1

The Correct Option is C

Step 1: Read the layout from the figure
Electrode order along a line is \(\mathrm{C1}\), \(\mathrm{C2}\), \(\mathrm{P1}\), \(\mathrm{P2}\) with \emph{equal spacing} \(a\) between adjacent electrodes.
Step 2: Recognize dipoles
- \(\mathrm{C1}\)–\(\mathrm{C2}\) form the \emph{current dipole} of length \(a\).
- \(\mathrm{P1}\)–\(\mathrm{P2}\) form the \emph{potential dipole} of length \(a\).
- The gap between the two dipoles is the spacing between \(\mathrm{C2}\) and \(\mathrm{P1}\), which is also \(a\). Hence the centers of the two dipoles are separated by \(2a\) (from \(x=\tfrac{a}{2}\) to \(x=\tfrac{5a}{2}\)).
Step 3: Match with the dipole–dipole definition
In a Dipole–Dipole array, two equal-length dipoles (current and potential) are laid out colinearly, and the center-to-center separation is \(n a\) where \(n\) is an integer (\(n\ge 1\)).
Here each dipole length \(= a\) and center-to-center separation \(= 2a\) \(\Rightarrow\) \(n=2\). This precisely matches a dipole–dipole configuration with \(n=2\).
Step 4: Rule out other arrays
- Wenner: Order is typically \(\mathrm{C1}\)–\(\mathrm{P1}\)–\(\mathrm{P2}\)–\(\mathrm{C2}\) with equal spacing; the potential pair sits \emph{between} the current electrodes. Not the case here.
- Schlumberger: Current electrodes far apart, potential electrodes close together near the center; spacings are unequal. Not the case here.
- Pole–Pole: Uses one current and one potential electrode with remote returns at infinity. Not applicable. \[ \boxed{\text{Therefore, the array is Dipole–Dipole (with } n=2\text{).}} \]