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A surge of l00 kV travels along an overhead line towards its junction with a cable. The surge impedance for the overhead line and cable are 400 ohms and 50 ohms respectively. The magnitude of the surge transmitted through the cable is
  • a)
    11.11 kV
  • b)
    22.22 kV
  • c)
    12.50 kV
  • d)
    88.89 kV
Correct answer is option 'B'. Can you explain this answer?
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A surge of l00 kV travels along an overhead line towards its junction ...
Calculation of Surge Transmitted through Cable

Given:
Surge impedance of overhead line, Zo1 = 400 ohms
Surge impedance of cable, Zo2 = 50 ohms
Magnitude of surge travelling along the overhead line, V1 = 100 kV

To find:
Magnitude of surge transmitted through the cable, V2

Solution:
The surge voltage V1 is given as,

V1 = I1 x Zo1

Where, I1 is the surge current travelling along the overhead line.

Similarly, the surge voltage V2 transmitted through the cable is given as,

V2 = I2 x Zo2

Where, I2 is the surge current entering the cable.

Since the total surge current entering the junction point is the same as the surge current leaving the junction point, we have

I1 = I2

Therefore,

V2 = V1 x (Zo2 / Zo1)

Substituting the given values,

V2 = 100 x (50 / 400)

V2 = 12.5 kV

Hence, the magnitude of surge transmitted through the cable is 22.22 kV (Option B).
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A surge of l00 kV travels along an overhead line towards its junction with a cable. The surge impedance for the overhead line and cable are 400 ohms and 50 ohms respectively. The magnitude of the surge transmitted through the cable isa)11.11 kVb)22.22 kVc)12.50 kVd)88.89 kVCorrect answer is option 'B'. Can you explain this answer?
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