Question E5D01:
What is the result of conductor skin effect?  

Choices:  
A: Resistance increases as frequency increases because RF current flows closer to the surface  
B: Resistance decreases as frequency increases because electron mobility increases  
C: Resistance increases as temperature increases because of the change in thermal coefficient  
D: Resistance decreases as temperature increases because of the change in thermal coefficient    

Correct Answer is  A: Resistance increases as frequency increases because RF current flows closer to the surface  

To understand skin effect, remember that AC current crowds toward a conductor’s surface as frequency increases. That shrinks the effective cross-sectional area carrying current, so resistance goes up.

Why the correct answer is correct (A):
- Skin effect forces RF current into a thin layer near the surface. The effective area becomes smaller, so by $R = \rho L / A$, the resistance increases with frequency.
- The “skin depth” is the thickness of that current-carrying layer:
  $$\delta = \sqrt{\frac{2\rho}{\omega \mu}} = \frac{1}{\sqrt{\pi f \mu \sigma}}$$
  where $\rho$ is resistivity, $\sigma$ is conductivity, $\mu$ is permeability, $f$ is frequency, and $\omega = 2\pi f$.
- Since $\delta \propto 1/\sqrt{f}$, the AC resistance for a round conductor increases approximately as:
  $$R_{ac} \propto \frac{1}{\delta} \propto \sqrt{f}$$
- For a round wire when $\delta \ll r$ (wire radius $r$):
  $$R_{ac} \approx \frac{\rho L}{2\pi r\,\delta} \quad\Rightarrow\quad \frac{R_{ac}}{R_{dc}} \approx \frac{r}{2\delta}$$

Why the other choices are incorrect:
- B: “Resistance decreases as frequency increases…” Incorrect. Skin effect does the opposite; it increases resistance with frequency. Electron mobility is not the governing factor here.
- C: “Resistance increases as temperature increases…” While true for metals, that’s due to temperature coefficient, not skin effect. The question is specifically about frequency-dependent behavior.
- D: “Resistance decreases as temperature increases…” Incorrect for typical metals (they have a positive temperature coefficient). Also unrelated to skin effect.

Useful rules of thumb:
- Copper skin depth: at $1$ MHz, $\delta \approx 66\,\mu\text{m}$. More generally:
  $$\delta_{\text{Cu}} \approx \frac{66}{\sqrt{f_{\text{MHz}}}}\,\mu\text{m} \approx \frac{0.0026}{\sqrt{f_{\text{MHz}}}}\,\text{inches}$$
- Most RF current flows within about $3\delta$ of the surface. Silver or copper plating thicker than a few skin depths carries essentially all the RF current.