Rework Problem 13.18 for a lossy line with a constant series resistance \(\mathrm{R}=0.3 \Omega / \mathrm{km}\). Lump half of the total resistance at each end of the line.

Problem 13.18

For the circuit given in Problem 13.3, replace the circuit elements by their discrete-time equivalent circuits and write nodal equations in a form suitable for computer solution of the sending-end and receiving-end voltages. Give equations for all dependent sources. Assume \(\mathrm{E}=1000 \mathrm{~V}, \mathrm{~L}_{\mathrm{R}}=\) \(20 \mathrm{mH}, Z_{c}=100 \Omega, v=2 \times 10^{8} \mathrm{~m} / \mathrm{s}, l=40 \mathrm{~km}\), and \(\Delta t=0.02 \mathrm{~ms}\).