A t-line with the far end open-circuited is not equivalent to a capacitor at all.  The t-line has distributed series inductance and distributed parallel capacitance.  Replace your pulse generator with a sine wave generator and sweep the frequency up from DC while measuring the voltage across and the current into the t-line.  You will find that as the frequency is increased, the impedance looking into the t-line alternates between pure capacitance and pure inductance.  No capacitor that I know of behaves this way.  Finally, consider this:  let the length of your t-line go to infinity.  In the limit, your open-circuited t-line looks like a 50 ohm resistor.      
 
 ::