Derivation of telegrapher's equations

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In deriving the telegrapher's equations, there is confusion regarding the arrangement of shunt capacitance and shunt conductance, specifically whether they are in parallel. The discussion highlights that in Pozar's derivations, he assumes they are parallel with the voltages at each end. There is uncertainty about the voltage designation 'u' used for both the capacitor and resistor, raising questions about whether it refers to u(x,t) and how it relates to u(x+dc,t). Clarification is sought on the parallel relationships in the context of integrated circuits. The need for a clearer understanding of these concepts in circuit analysis is emphasized.
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When deriving telegrapher's equations using Kirchhoff current/voltage laws (this equivalent circuit), are the shunt capacitance and shunt conductance in parallel? I assume not, and if not, are they in parallel with the voltages at each corresponding end? I am confused by this; in Pozar's derivations, he assumes the latter when using Kirchhoff current law. I always have trouble determining what is parallel with what, especially in ICs. Can anyone elucidate this for me?
 
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Thanks for the derivation although I think my questions are still unanswered. When calculating the losses through the resistor and capacitor, he uses voltage 'u' for both. Is this u(x,t)? Both the capacitor and resistor are at this voltage, so in parallel? What about the voltage at u(x+dc,t)?
 
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