Electrode resistance
Plate electrode resistance
- where
- radius of the equivalent disc (m)
- area of one face of the plate (m²)
- plate resistance at depth h (Ω)
- soil resistivity (Ω·m)
- depth of burial (m)
- resistance of the same plate at the surface (BS 7430 form) (Ω)
Explain this equation
Estimates the resistance of a buried plate or flat steel foundation by treating it as a circular disc of the same face area.
r is the radius of that equivalent disc. ρ/(8r) is the resistance of a disc deep in the soil, where current leaves both faces into an unbounded medium. The bracket raises this towards ρ/(4r) as the plate approaches the surface, because the ground surface cuts off half the space. R0 is the surface value used in BS 7430.
Resistance depends on the linear size r, not the area, because current crowding near the edges controls the result. That is why plates use material less efficiently than rods or tape.
A 1 m² plate in 100 Ω·m soil is about 44 Ω at the surface and 28 Ω at 0.6 m. Quadrupling the area only halves R.
Watch out: the 2.5h term is an empirical blend between the two limits, so treat intermediate depths as estimates.
Resistance of a buried plate (or a sheet-steel foundation) treated as an equivalent circular disc.
Enter your values to see the result.
Good to know
EREC S34 formula R2 gives ρ/(8r)·[1 + r/(2.5h + r)], which runs from ρ/(4r) for a plate at the surface to ρ/(8r) for a deep plate (a disc in infinite soil). BS 7430 gives the surface value (ρ/4)√(π/A), which equals ρ/(4r). A 1 m² plate in 100 Ω·m soil at 0.6 m is about 28 Ω. Resistance falls with the linear size, not the area, so plates are an inefficient use of copper compared with rods or tape.
Common mistake
Expecting a large plate to give a low resistance. Doubling the area only reduces R by about 30 %.
Limits
Uniform soil; plate treated as an equivalent disc of the same face area. Plates larger than about 1.2 m × 1.2 m are not recommended by BS 7430; several plates should be at least 2 m apart.
Sources
For competent high-voltage engineers. Results are calculations from the published methods shown and depend entirely on the data you enter. They are not a substitute for a system study, manufacturer data, the applicable standards and Engineering Recommendations, or your organisation’s safety rules. Never use a result to justify working on or near live HV equipment.