Correct Answer - Option 1 : 50 Ω
Surge impedance:
The surge impedance or characteristic impedance of a long transmission line is given by,
\({Z_s} = \sqrt {\frac{Z}{Y}} = \sqrt {\frac{{R + j\omega L}}{{G + j\omega C}}} \)
Where,
Z is series impedance per unit length per phase
Y is shunt admittance per unit length per phase
In case of a lossless line (i.e. R = 0, G=0), the surge impedance is given by
\({Z_s} = \sqrt {\frac{L}{C}} \)
- Surge impedance does not depend upon the length of the transmission line.
- Surge impedance depends on the characteristics of the transmission line like diameter & spacing between the conductors.
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So that surge impedance of 100 km and 50km long underground cable is 50 Ω.
Surge impedance loading (SIL):
Surge impedance loading is defined as the power load in which the total reactive power of the lines becomes zero. The reactive power generated by the shunt capacitance is consumed by the series inductance of the line.
\(SIL = \frac{{{V^2}}}{{{Z_S}}}\;\;\;MW\)
