---
title: "Methods of earth resistivity measurement"
subject: "High Voltage Engineering"
chapter: 2
key: "semester_8/high_voltage_engineering:earth-resistivity-methods"
source: https://www.bctengineer.com/q/semester_8/high_voltage_engineering/earth-resistivity-methods
site: BCT Engineering
---

# Methods of earth resistivity measurement

High Voltage Engineering · Chapter 2: Electric Shocks

- Asked in: 2073 Bhadra, 8 marks
- Answer checked by Claude Opus 5.5 (high effort) on 2026-10-14
- Page: https://www.bctengineer.com/q/semester_8/high_voltage_engineering/earth-resistivity-methods
- Whole chapter: https://www.bctengineer.com/md/semester_8/high_voltage_engineering/chapter-2

## Question

Explain different methods of earth resistivity measurement with diagrams.

## Short answer

Wenner method: four equal-spaced electrodes, resistivity ρ = 2πaR. Schlumberger method: close potential electrodes, ρ=πc(c+d)R/d. Driven-rod method: measure rod resistance by fall-of-potential, compute ρ = 2πLR/(ln(8L/d)−1). Use AC or reversing DC to avoid polarization.

## Answer

Earth resistivity $\rho$ is measured to design earthing systems (substation grids, tower footings). The common methods use an earth tester that injects current $I$ and measures voltage $V$, giving $R = V/I$.

#### 1. Wenner four-electrode method
Four electrodes are placed in a straight line at equal spacing $a$, driven to a depth $b \ll a$. Current is passed between the outer pair (C1, C2); voltage is measured between the inner pair (P1, P2).
```text
   C1      P1      P2      C2
 --|-------|-------|-------|--
   |<- a ->|<- a ->|<- a ->|
```
Potential due to a point source at the surface is $\frac{\rho I}{2\pi r}$. By superposition:
$$
V = \frac{\rho I}{2\pi}\left[\left(\frac{1}{a}-\frac{1}{2a}\right) - \left(\frac{1}{2a}-\frac{1}{a}\right)\right] = \frac{\rho I}{2\pi a}
$$
$$
\rho = 2\pi a R
$$
Readings at increasing spacing give resistivity at increasing depth (about depth $a$).

#### 2. Schlumberger (Schlumberger–Palmer) method
The potential electrodes are kept close together (spacing $d$), and the current electrodes are placed at distance $c$ outside each potential electrode. Only the current electrodes are moved for deeper readings, so it is faster and more sensitive for large spacings.
```text
   C1          P1  P2          C2
 --|-----------|---|-----------|--
   |<--- c --->|<d>|<--- c --->|
```
$$
\rho = \frac{\pi c(c+d)R}{d}
$$
For $c = d = a$ this gives $\rho = 2\pi aR$, the Wenner case.

#### 3. Driven-rod (three-point / variation-of-depth) method
A test rod of length $L$ and diameter $d$ is driven into the soil, and its resistance $R$ is measured by the fall-of-potential method using a current probe C (far away, at least 5–10 times rod length) and a potential probe P at about 62% of that distance.
```text
  Earth tester
   E      P            C
 --|------|------------|--
   |<-0.62D->|
   |<-------- D ------->|
   test rod
```
$$
\rho = \frac{2\pi L R}{\ln\left(\dfrac{8L}{d}\right) - 1}
$$
Repeating with the rod driven deeper gives the change of resistivity with depth. It is simple and suited to small areas but measures only the soil near the rod.

#### Practical points
- Take readings in several directions and at several spacings; use the dry-season (highest) value for design.
- Use AC or reversing DC to avoid polarisation and errors from stray currents.
- Keep test leads away from buried metal pipes and cables, which distort the readings.

## Check yourself

The answer's key points as multiple-choice questions, with the correct option and why.

1. In the Wenner method with spacing a:
   A. rho = pi*a*R
   B. rho = 2*pi*a*R
   C. rho = R/(2*pi*a)
   D. rho = 4*pi*a*R
   Answer: B. Superposition gives V = rho*I/(2*pi*a). (Key point: Wenner result)

2. What is distinctive about the Schlumberger method?
   A. Potential electrodes are close together and only current electrodes are moved outward
   B. All four electrodes move equally
   C. Only one electrode is used
   D. Uses a driven rod
   Answer: A. It is faster and more sensitive at large spacings; rho = pi*c(c+d)R/d. (Key point: Schlumberger layout)

3. For c = d = a, the Schlumberger formula gives:
   A. rho = pi*a*R
   B. rho = 4*pi*a*R
   C. rho = 2*pi*a*R, the Wenner case
   D. rho = 0
   Answer: C. pi*a*(2a)/a*R = 2*pi*a*R. (Key point: Schlumberger-Wenner link)

4. In the driven-rod method the potential probe is placed at about:
   A. 10% of the distance
   B. 62% of the distance to the current probe
   C. 100% of the distance
   D. Next to the rod
   Answer: B. The 62% rule gives the true rod resistance. (Key point: Fall of potential)

## Related in High Voltage Engineering

- [Wenner's method of earth resistivity measurement](https://www.bctengineer.com/question.md?key=semester_8%2Fhigh_voltage_engineering%3Awenner-earth-resistivity) — High Voltage Engineering, chapter 2, asked 3×
- [Why measure earth resistivity](https://www.bctengineer.com/question.md?key=semester_8%2Fhigh_voltage_engineering%3Aearth-resistivity-necessity) — High Voltage Engineering, chapter 2

## Related in other subjects

- [Soil resistivity and reducing earth resistance](https://www.bctengineer.com/question.md?key=semester_6%2Fswitchgear_and_protection%3Asoil-resistivity-earth-resistance) — Switchgear and Protection, chapter 5