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For a stranded conductor the ratio of GMR to actual radius is
Equal to 1
More than 1
Equal to $0.778$
Less than $0.778$
Less than $0.778$
The Geometric Mean Radius (GMR) of a stranded conductor is less than the actual radius (r) because it accounts for the internal magnetic flux linkages of the strands ┬╖ For a single solid circular conductor, the GMR is $0.7788r$, whereas for stranded conductors, the arrangement of strands leads to an even smaller effective radius.
The Geometric Mean Radius (GMR) of a stranded conductor is less than the actual radius (r) because it accounts for the internal magnetic flux linkages of the strands ┬╖ For a single solid circular conductor, the GMR is $0.7788r$, whereas for stranded conductors, the arrangement of strands leads to an even smaller effective radius.
GMR=0.7788r тАФ GMR for a solid circular conductor
L=2├Ч10тИТ7ln(GMRDeqтАЛтАЛ) тАФ Inductance of a transmission line
The GMR, or DsтАЛ, is a fictitious radius that replaces the actual physical radius in inductance calculations to account for internal flux ┬╖ For a stranded conductor, the GMR is calculated using the Geometric Mean Distance (GMD) of all internal strands and the self-GMD of each individual strand ┬╖ Because the strands are distributed over a larger area while sharing current, the effective internal flux linkage per unit of physical radius is reduced compared to a solid conductor, resulting in a ratio GMR/r<0.7788.
GMR is a measure of the effective radius of a conductor regarding magnetic flux linkage.
For a solid conductor, the internal flux linkage results in a GMR factor of eтИТ0.25тЙИ0.7788.
Stranded conductors have lower internal inductance than solid conductors of the same diameter, leading to a ratio lower than $0.7788$.
The GMR is always less than the physical radius r.
Reduces internal inductance of the conductor.
Provides flexibility and mechanical strength in transmission line design.
Increases AC resistance due to skin effect.
Requires more complex geometric calculations for large bundles.
High-voltage AC transmission lines.
Distribution network conductor sizing.
The factor $0.7788isderivedfrome^{-1/4}$, which represents the self-inductance contribution of a solid cylinder.
Option C (0.778) specifically refers to the ratio for a single solid conductor, not a multi-strand stranded conductor.
D is correct тАФ The GMR for a stranded conductor is always less than $0.7788$ times its outer radius due to the specific arrangement and flux distribution of the individual strands.
Always remember that GMR deals with magnetic flux linkages; if a question asks about capacitance, use the actual physical radius r, not GMR.