telegrapher's equations

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 of the equations 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.