Previous Year Question
An overhead transmission line has inductance of 0.9 mH/km and capacitance of 10 nF/km. The surge impedance of the line will be
Correct answer: B
Explanation
For a nearly lossless overhead line, surge impedance Z0=√(L/C). With L=0.9 mH/km and C=10 nF/km, L/C=0.9×10⁻³/(10×10⁻⁹)=9×10⁴, so Z0=300 Ω. Thus option B.
Formula
Z0=√(L/C)=√(0.9×10⁻³/10×10⁻⁹)=300Ω
Step-by-step solution
Correct Answer
B — 300Ω
Concept and Reasoning
For a nearly lossless overhead line, surge impedance Z0=√(L/C). With L=0.9 mH/km and C=10 nF/km, L/C=0.9×10⁻³/(10×10⁻⁹)=9×10⁴, so Z0=300 Ω. Thus option B.
Calculation / Key Relation
Z0=√(L/C)=√(0.9×10⁻³/10×10⁻⁹)=300Ω
Exam Takeaway
Use per-unit-length L and C in consistent units; the km cancels.
Common Mistake
Do not use √(C/L) or forget the milli/nano conversion.
Common mistake
Do not use √(C/L) or forget the milli/nano conversion.
Exam tip
Use per-unit-length L and C in consistent units; the km cancels.
Quick method
Use per-unit-length L and C in consistent units; the km cancels.