Question E9F03:
Why is the electrical length of a coaxial cable longer than its physical length?  

Choices:  
A: Skin effect is less pronounced in the coaxial cable  
B: Skin effect is more pronounced in the coaxial cable  
C: Electromagnetic waves move faster in coaxial cable than in air  
D: Electromagnetic waves move more slowly in a coaxial cable than in air    

Correct Answer is  D: Electromagnetic waves move more slowly in a coaxial cable than in air  

To understand “electrical length,” think in terms of phase delay or fraction of a wavelength. A cable’s electrical length is longer than its physical length when signals travel slower inside it, so a given physical length corresponds to a larger fraction of a wavelength (more phase shift).

Why D is correct (Electromagnetic waves move more slowly in a coaxial cable than in air):
- Coax has a dielectric between the conductors, which slows the wave’s velocity.
- The velocity in the cable is $v = VF \cdot c$ with $0 < VF < 1$, so the wavelength inside the cable is shorter: $\lambda_{\text{coax}} = v/f = VF \cdot \lambda_0$.
- Electrical length in wavelengths is $L_e = L/\lambda_{\text{coax}} = L/(VF \cdot \lambda_0)$, which is larger than $L/\lambda_0$ when $VF < 1$. Thus the cable “looks” longer electrically.

Why the other choices are incorrect:
- A: “Skin effect is less pronounced” — Skin effect affects resistance/attenuation, not the phase velocity that determines electrical length.
- B: “Skin effect is more pronounced” — Same issue: it changes loss, not the wave speed in the dielectric (at HF/VHF exam context).
- C: “Waves move faster in coax than in air” — Opposite of reality; the dielectric always reduces velocity below $c$.

Useful formulas and rules of thumb:
- Wave velocity: $v = \dfrac{1}{\sqrt{LC}} \approx \dfrac{c}{\sqrt{\epsilon_r}}$ (for non-magnetic dielectrics).
- Velocity factor: $VF = \dfrac{v}{c} \approx \dfrac{1}{\sqrt{\epsilon_r}}$.
- Wavelength in coax: $\lambda_{\text{coax}} = VF \cdot \lambda_0 = \dfrac{VF \cdot c}{f}$.
- Electrical length (degrees): $\theta = 360^\circ \dfrac{L}{\lambda_{\text{coax}}} = 360^\circ \dfrac{f L}{VF \cdot c}$.
- Typical $VF$ values:
  - Solid polyethylene: $VF \approx 0.66$
  - Foam polyethylene: $VF \approx 0.80$–$0.85$
  - PTFE (Teflon): $VF \approx 0.69$–$0.70$

Bottom line: A dielectric in coax slows the wave, shortening $\lambda$ inside the cable and making a given physical length correspond to a longer electrical length.