Exercise 11.2 What the wire?

a)

An answer:
$Z_{\mathit{res}}(\mathit{j\omega })=R+\mathit{j\omega l}\cdot 2\mathit{nH}∕\mathit{mm}$ with $l$ the total wire length in mm.

b)

An answer:
At the limit:

$$\begin{array}{llll}\hfill |Z(\mathit{j\omega })|& =\sqrt{R^2+{\omega }^2{L}^2}& \hfill & \\ \hfill & =\sqrt{2}\cdot R& \hfill & \end{array}$$

leading to:

$$\begin{array}{llll}\hfill & R^2+{\omega }^2{L}^2=2\cdot R^2& \hfill & \\ \hfill {\omega }_{\mathit{max}}& =\frac{R}{L}& \hfill & \\ \hfill f_{\mathit{max}}& =200\mathit{MHz}& \hfill & \end{array}$$

c)

An answer:
Hmm... that’s pretty close to $R=100\mathrm{\Omega }$!

d)

An answer:
Hmm... that’s probably larger than anything you’d ever build as audio amplifier.