To start with, it is good to highlight that there are two fundamentally different quantities that are often incorrectly used in parallel and interchangeably:

• Resistance
  • System specific quantity > Longer the path between in/out, the higher the value
  • Unit: Ohm or the greek letter Ω
  • Often used for practical purposes
• Resistivity
  • Material property > calculation includes the dimensions of the measurement system
  • Unit: Ohm*m or Ωm, for surface resistivity also Ohm/sq or Ω/□
  • Used for design calculations, characterization and classification of materials
  • For non-metallic conductors Ohm*cm is often preferred due to their relatively high resistances.

Resistance of a solid, homogeneous cylinder shape can be calculated as

R = ρ*L/A

, where ρ is the electrical resistivity of the material, L is the length of the shape and A is the cross-sectional area. From the formula it is evident that R doubles if length doubles. The volume resistivity can be expressed as

ρ = R*A/L

, where R can be replaced with R = U/I from the Ohm’s law to the following form

ρ = UA/IL,

, where U is voltage (V) and I is electric current (A).

This leads to a problemacy. If resistance can be easily measured alongside with voltage, current and dimensions – why is there a need for so many different probes and measurement fixtures instead of using just the metallic pointy ones that comes with even the cheapest multimeters on the market?

That is due to contact resistance, an annoyance that is always part of the equation – and if not not taken into account, can possibly be significant enough to mask the actual resistivity of the material completely. Typical way to take it into account is to carry out the measurements with a more complex 4-point setup.

The measured resistance value measured between a known distance is likely to vary depending on measurement details. Such factors could be the measurement method, tools, ambient conditions (%RH) and the operator for example.

Resistance in its essence expresses how an element in the circuit restricts the flow of electricity – thus it is evident that the method that gives the lowest value is the most correct, unless the method externally biases the material characteristics. When carrying out a simple 2-point resistance measurement, the value measured is actually three resistance values in series:

• contact resistance between positive electrode and the sample
• Intrinsic resistance of the sample
• contact resistance between the sample and the negative electrode