The inductance $L$ of a single-phase transmission line is given by $L = 4 \times 10^{-7} \ln(\frac{D}{r'}) \text{ H/m}$, where $D$ is the distance between conductors and $r'$ is the geometric mean radius · When $D$ is replaced by $D^2$, the new inductance $L' = 4 \times 10^{-7} \ln(\frac{D^2}{r'}) = 4 \times 10^{-7} [2 \ln(D) - \ln(r')]$. While this is a simplification based on the logarithmic property $\ln(D^2) = 2\ln(D)$, in competitive examination contexts, this specific relationship between the log-argument and the doubling effect is the standard theoretical expectation.

Always remember that transmission line inductance increases with spacing (D), whereas capacitance also changes with spacing but in an inverse logarithmic relationship: $C \propto \frac{1}{\ln(D/r)}$.