From the results of Example 13.2, plot the voltage and current profiles along the line at times \(\tau / 2, \tau\), and \(2 \tau\). That is, plot \(v(x, \tau / 2)\) and \(i(x, \tau / 2)\) versus \(x\) for \(0 \leqslant x \leqslant 1\); then plot \(v(x, \tau), i(x, x), v(x, 2 \tau)\), and \(i(x, 2 x)\) versus \(x\).

Example 13.2

The receiving end is open. The source voltage at the sending end is a step \(e_{\mathrm{G}}(t)=\) \(\mathrm{E} u_{-1}(t)\), with \(\mathrm{Z}_{\mathrm{G}}(s)=\mathrm{Z}_{c}\).

(a) Determine \(v(x, t)\) and \(i(x, t)\).

(b) Plot the voltage and current versus time \(t\) at the center of the line.