Characteristic Impedance from Per-Unit-Length L and C for a Coaxial Line A coaxial line has per-unit-length parameters L = 500 nH/m and C = 50 pF/m. Compute the characteristic impedance Z0.

Introduction / Context:For a lossless (or low-loss) transmission line, the characteristic impedance Z0 depends on its per-unit-length inductance L and capacitance C.

Given Data / Assumptions:

• L = 500 nH/m = 500 × 10^-9 H/m
• C = 50 pF/m = 50 × 10^-12 F/m
• Line is treated as lossless for Z0 calculation.

Concept / Approach:

For a lossless line, Z0 = sqrt(L / C). We will compute this directly using the given values.

Step-by-Step Solution:

Verification / Alternative check:

Dimensional check: sqrt(H/F) has units of ohms. Numerical value agrees with typical coax impedances when L/C ratio is 10^4.

Why Other Options Are Wrong:

500 Ω, 250 Ω, 50 Ω, and 75 Ω do not satisfy Z0 = sqrt(L/C) for the supplied numbers.

Common Pitfalls:

Arithmetic slips with scientific notation; forgetting that Z0 depends on the ratio L/C, not on frequency for the ideal lossless case.

Final Answer:

100 Ω.