DC Resistance Matrices

The resistance matrix gives the relationship between voltage drops and currents. For instance, the transmission structure shown below consists of two regular conductors, one of which has multiple sources of current.

The voltage drops are given by:

ΔV₁ = i₁R₁₁ + i₂R₁₂

ΔV₂ = i₂R₂₂ + i₁R₁₂

ΔV₃ = i₃R₃₃

This can be expressed in matrix form as:

where:

• R₁₁, R₂₂, and R₃₃ are the self-resistances of each current path.
• R₁₂ is the mutual resistance between current paths 1 and 2. For DC resistance matrices, the mutual resistance is only nonzero for current paths within the same net (that is, conductor nets that have multiple sources of current).