Rework Example 13.6 if the overhead line and cable are interchanged. That is, \(\mathrm{Z}_{\mathrm{A}}=100 \Omega, v_{\mathrm{A}}=2 \times 10^{8} \mathrm{~m} / \mathrm{s}, l_{\mathrm{A}}=20 \mathrm{~km}, \mathrm{Z}_{\mathrm{B}}=400 \Omega, v_{\mathrm{B}}=\) \(3 \times 10^{8} \mathrm{~m} / \mathrm{s}\), and \(l_{\mathrm{B}}=30 \mathrm{~km}\). The step voltage source \(e_{\mathrm{G}}(t)=E u_{-1}(t)\) is applied to the sending end of line \(\mathrm{A}\) with \(\mathrm{Z}_{\mathrm{G}}=Z_{\mathrm{A}}=100 \Omega\), and \(\mathrm{Z}_{\mathrm{R}}=\) \(2 \mathrm{Z}_{\mathrm{B}}=800 \Omega\), at the receiving end. Draw the lattice diagram for \(0 \leq t \leq\) \(0.6 \mathrm{~ms}\) and plot the junction voltage versus time \(t\).

Example 13.6

As shown in Figure 13.10, a single-phase lossless overhead line with \(\mathrm{Z}_{\mathrm{A}}=400 \Omega\), \(v_{\mathrm{A}}=3 \times 10^{8} \mathrm{~m} / \mathrm{s}\), and \(l_{\mathrm{A}}=30 \mathrm{~km}\) is connected to a single-phase lossless cable with \(Z_{\mathrm{B}}=100 \Omega, v_{\mathrm{B}}=2 \times 10^{8} \mathrm{~m} / \mathrm{s}\), and \(l_{\mathrm{B}}=20 \mathrm{~km}\). At the sending end of line A, \(e_{g}(t)=\mathrm{E} u_{-1}(t)\) and \(\mathrm{Z}_{\mathrm{G}}=\mathrm{Z}_{\mathrm{A}}\). At the receiving end of line \(\mathrm{B}, \mathrm{Z}_{\mathrm{R}}=2 \mathrm{Z}_{\mathrm{B}}=200 \Omega\). Draw the lattice diagram for \(0 \leq t \leq 0.6 \mathrm{~ms}\) and plot the voltage at the junction versus time. The line and cable are initially unenergized.

Figure 13.10

Transcribed Image Text:

Line A ZA VA Line B ZB