Telegrapher's equations are a set of two coupled, linear equations that predict the voltage and current distributions on a linear electrical transmission line.

These equations are important because they allow transmission lines to be analyzed using circuit theory.

They result from, like all other equations, from Maxwell's Laws of Electromagnetism.

Transmission Line Lumped Element Model

(See the Wikipedia article on Characteristic Impedance too)

It can be modeled as infinite capacitors and inductors along the direction of field propagation.
The characteristic impedance of the infinite path can be modeled as a resistance,

\(\large Z_0 = R = \sqrt{\dfrac{L}{C}}\) (for radio frequencies; use general formula for audio frequencies)

So we can remove the capacitor and inductor chain and replace it with a resistor.
This is how the circuit will perceive the current, until it reaches the end and returns with the information.
Then it will proceed to the next step of negotiation, and repeat. Just like solving a maze, but of circuit paths here.
The final state is called the steady state.

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