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Inductance of single phase two wire line is given by
$0.4 \ln(D/r) \text{ mH/km}$
$0.55 \ln(D/r) \text{ mH/km}$
$0.4 \ln(r/D) \text{ mH/km}$
$0.55 \ln(r/D) \text{ mH/km}$
$0.4 \ln(D/r) \text{ mH/km}$
The inductance of a single-phase two-wire transmission line is derived from the flux linkages of the conductors ┬╖ For two parallel conductors of radius 'r' separated by a distance 'D', the total inductance per unit length is the sum of internal and external inductances, resulting in a value of approximately $0.4 \ln(D/r)$ mH/km.
The inductance of a single-phase two-wire transmission line is derived from the flux linkages of the conductors ┬╖ For two parallel conductors of radius 'r' separated by a distance 'D', the total inductance per unit length is the sum of internal and external inductances, resulting in a value of approximately $0.4 \ln(D/r)$ mH/km.
L=4├Ч10тИТ7ln(rтА▓DтАЛ)┬аH/m тАФ Fundamental inductance formula using GMR (rтА▓)
L=0.4ln(rDтАЛ)┬аmH/km тАФ Practical engineering approximation
The total inductance L is calculated by considering the flux linkage of each conductor ┬╖ The formula L=4├Ч10тИТ7ln(D/rтА▓)┬аH/m is converted to mH/km, where rтА▓ is the geometric mean radius (GMR) of the conductor (rтА▓=reтИТ1/4тЙИ0.7788r) ┬╖ Substituting these constants leads to the standard engineering approximation $0.4 \ln(D/r)$ mH/km.
Inductance increases logarithmically as the distance between conductors (D) increases.
Inductance decreases as the radius (r) of the conductor increases.
The factor 0.7788 represents the internal flux linkage effect accounted for in the conversion from rтА▓ to r.
Transmission line inductance is a key parameter for calculating voltage drops and stability.
Provides a simple logarithmic relationship for system design.
Essential for modeling impedance in power systems.
Assumes non-magnetic conductors and uniform current distribution.
Becomes complex with bundles or multiple-phase configurations.
Design of distribution and transmission lines.
Calculation of power factor and voltage regulation.
The constant 0.4 arises from (2├Ч2├Ч10тИТ7)├Ч1000 to convert Henries per meter to mH/km.
Option C and D are incorrect as the argument of the natural logarithm must be greater than 1 (D > r) for a positive inductance value.
A is correct тАФ The inductance of a single-phase two-wire line is given by the expression $0.4 \ln(D/r)$ mH/km.
Remember that capacitance formula uses a similar logarithmic form but involves ln(D/r) in the denominator, highlighting the inverse relationship between L and C parameters in transmission lines.