### telegrapher's equations

(two equations describing a transmission line)

The **telegrapher's equations** are a pair of partial differential equations
describing the electrical characteristics of an electrical transmission line,
taking into account electrical resistance and inductance
along the conductor(s) and resistance and capacitance
between them, or between the conductor and ground.
They refer to alternating current: for direct current, with no
variation over time, each effectively simplifies to the
transmission line's derivative of **Ohm's law** (V=IR).
Naturally, they are derivable from Maxwell's equations.
The equations:

∂V ∂I
—— = -L —— - RI
∂x ∂t
∂I ∂V
—— = -C —— - GI
∂x ∂t

- t - time.
- x - position along the length of the line.
- V - voltage, a function of x and t.
- I - current, a function of x and t.
- L - inductance along the line.
- R - resistance along the line.
- C - capacitance between lines.
- G - conductance (1/resistance) between lines.

L, R, C, and G are "per distance",
e.g., "so much per meter of transmission cable",
and they each depend upon the characteristics of the
transmission line and to the AC frequency being
propagated.

The telegraphers equations can be used for phenomena
analogous to electrical transmission cables,
including some astrophysical jets.

(*equation,physics,electricity,magnetism*)
**Further reading:**

https://en.wikipedia.org/wiki/Telegrapher%27s_equations

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