Incremental model of a transmission line

A small length $\Delta x$ of a uniform line is modelled with series resistance $R\Delta x$ and inductance $L\Delta x$, and shunt conductance $G\Delta x$ and capacitance $C\Delta x$ ($R, L, G, C$ per unit length).

   i(x)   R.dx      L.dx         i(x+dx)
 o──>──[/\/\/]──[ coil ]──┬───────┬────o
 +                        │       │    +
                        [G.dx]  [C.dx]
 v(x)                     │       │   v(x+dx)
 -                        │       │    -
 o────────────────────────┴───────┴────o
 |<──────────────── dx ─────────────>|

Series impedance per unit length $Z = R + j\omega L$; shunt admittance $Y = G + j\omega C$; characteristic impedance $Z_0 = \sqrt{Z/Y}$.