A coaxial RF cable has characteristic impedance Z0 = 50 Ω and capacitance per unit length C = 40 pF/m. Calculate the inductance per unit length L (in μH/m).

Introduction:In a lossless transmission line, the characteristic impedance relates inductance and capacitance per unit length. This problem applies the fundamental formula to compute L given Z0 and C for a coaxial cable.

Given Data / Assumptions:

• Z0 = 50 Ω
• C = 40 pF/m = 40 * 10^-12 F/m
• Assume lossless line so Z0 = sqrt(L / C)

Concept / Approach:For a lossless line, Z0 = sqrt(L / C). Rearranging gives L = Z0^2 * C. Convert units carefully so the final L is expressed in μH/m.

Step-by-Step Solution:

Verification / Alternative check:Dimensional check: Ω = sqrt(H/F); squaring Ω gives H/F; multiplying by F returns H, confirming unit consistency.

Why Other Options Are Wrong:

• A (1 μH/m): 10 times larger than the correct computed value.
• B (10 μH/m): off by two orders of magnitude.
• D (0.01 μH/m): ten times smaller than correct.

Common Pitfalls:Forgetting to square Z0; mishandling pico to base unit conversions; mixing nH and μH scales.

Final Answer:0.1 μH/m