GMR of 5-strand conductor, 0.5 cm strands

The GMR (self-GMD for inductance) of an $n$-strand conductor is the $n^2$-th root of the product of all inter-strand distances, with self-distance $r' = 0.7788r$.

        (4)   (5)
     (1)   (2)   (3)
  touching strands, centre spacing 2r

Data: $r = 0.5$ cm, $2r = 1$ cm, $r' = 0.7788 \times 0.5 = 0.3894$ cm.

Distances (cm)

Check: 7 + 1 + 2 = 10 pairs.

GMR

$$\begin{aligned} D_s &= \left[(r')^5 \times \left(1^7 \times 2 \times 1.732^2\right)^2\right]^{1/25} \\ &= \left[0.3894^5 \times 6^2\right]^{1/25} \\ &= 0.9557\ \text{cm} \end{aligned}$$

In terms of $r$: $D_s = 1.9114r$.

Answer: GMR $= 0.956$ cm.