Votage between ends of transmission line

I have two conductors forming a transmission line like in the figure below (left). Only B is grounded. What is the voltage between B and D at any given moment? If I use a transmission line model (right) then I can compute the voltage between A and B (v(t_0,0)) and the voltage bewteen C and D (v(t_0,L)) using transmission line equations but I can't find the voltage between B and D.

Edit 1: System connection (if it makes a difference): Let's say that A and B are connected to a voltage source and that C and D are a) left in open circuit b) connected to a resistance of value R

• Thanks I just added the external connections Commented Mar 6, 2020 at 16:35
• Thanks Ken, then the only way to affect the B to D conductor is just electrostatic since there is no current flow in the A to C conductor. Dr. Hortons paper should help. Sorry if I’m misunderstanding - I’m thinking 60Hz. Commented Mar 6, 2020 at 16:45
• You'll have a simple resistor ladder, consisting of resistances AC, R, and BD. Voltage across each resistor should be in proportion to its resistance. When R is infinity, then obviously all the voltage drop happens in R, and the AC and BD voltage drops will be zero. Commented Mar 6, 2020 at 19:51
• @Harper, since we're calling it a transmission line we should consider that it is reasonably long compared to the wavelength of whatever signals are exciting it. Say, at least 0.1 wavelengths, and possibly many wavelengths long. Commented Mar 7, 2020 at 6:35
• Thanks @Harper. What I perhaps didn't mention was that I'm dealing with signals with fast rise-times (~5ns) on a relatively long PCB. I get your suggestion of considering it a resistor ladder, that gives me an idea of the I*R drop, but how to account for the distributed L and C on the transmission line? Commented Mar 7, 2020 at 10:55