Final answer:
Without the full transmission line configuration, it is not possible to provide a numerical answer for the GMR, GMD, or the inductance per phase per kilometer of the line. The GMR is derived from the physical radius, and the inductance formula also requires the GMD, which depends on the configuration of the line.
Step-by-step explanation:
To calculate the GMR (Geometric Mean Radius) and the GMD (Geometric Mean Distance) for a power transmission line, we need additional information such as the configuration of the transmission line (e.g., single line, double line, distances between conductors, etc.). Since we only have the radius of the conductor, we can provide guidance on how the radius might be used in the overall calculation of inductance if the full configuration were known.
For a single, straight, homogeneous circular conductor like the one mentioned, with a radius of 0.250 cm, the GMR is typically derived from the physical radius, although for most practical calculations involving high voltage transmission lines, empirical formulas are used to adjust the GMR. However, without more specifics on the transmission line configuration, it is not possible to provide a numerical answer for the GMR, GMD or the inductance per phase per kilometer.
Inductance per phase per kilometer (L) can be approximately calculated by the equation:
L = (2 × 10^-7) × ln(GMD/GMR)
yet this formula requires the GMD, which depends on the distances between conductors in a multi-conductor system. With just the radius given, the formula can't be specifically applied.
Please provide the full transmission line configuration to give an accurate calculation for GMR, GMD, and inductance per phase per kilometer of the line.