For the case of a lossless line, how would the results of Problem 5.33 change?

In terms of $Z_c$, which is a real quantity for this case, express $P_{12}$ in terms $\left|I_1\right|$ and $\left|V_1\right|$.

Problem 5.33

Consider a long radial line terminated in its characteristic impedance \(Z_{c}\). Determine the following:

(a) \(V_{1} / I_{1}\), known as the driving point impedance.

(b) \(\left|V_{2}ight| / V_{1} \mid\), known as the voltage gain, in terms of \(\alpha \ell\).

(c) \(\left|I_{2}ight| /\left|/ I_{1}ight|\), known as the current gain, in terms of \(\alpha \ell\).

(d) The complex power gain, \(-S_{21} / S_{12}\), in terms of \(\alpha \ell\).

(e) The real power efficiency, \(\left(-\mathrm{P}_{21} / \mathrm{P}_{12}ight)=\eta\), terms of \(\alpha \ell\).

1 refers to sending end and 2 refers to receiving end. \(\left(S_{21}ight)\) is the complex power received at \(2 ; S_{12}\) is sent from 1.