It is now clear why is called a space-constant, it determines the voltage attenuation with distance.
Alternatively, we could demand that the current at x=0 be specified as . From (14) we see that
and since we get
The input resistance is the ratio of is thus
The input conductance for the semi-infinite cable is thus
Note: It is often convenient to introduce the dimensionless space variable, and the electrotonic length of the cable, This gets rid of all the divisions by in the exponentials and hyperbolic functions.