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  "body": "\n## Summary\n\nThe telegrapher's equations are a pair of linear first-order equations for the voltage and the current along an electrical transmission line.\nThey were developed by Oliver Heaviside to describe signals on telegraph cables.\nEliminating the current gives one second-order equation for the voltage, the telegraph equation, which is a damped [[wave equation|5EHD2XBQDG]].\nThe equations show how resistance and leakage make a signal both decay and spread out.\n\n## Explanations\n\n### L1 human\n\nA long cable has, per unit length, a resistance, an inductance, a capacitance between its wires, and a small leakage.\nA voltage pulse sent along the cable travels like a wave, but it loses strength and changes shape.\nThe telegrapher's equations describe this with two equations linking how voltage and current change in space and in time.\nWithout resistance and leakage, they reduce to the wave equation with speed $1/\\sqrt{LC}$, and a pulse travels without distortion.\n",
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