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When deriving the power lost during transmission, we use the following two formulae

  1. \$P=VI\$ where \$P\$ is the power that needs to be supplied, \$V\$ is the potential difference, and I is the current
  2. \$P_c=I^2R_c\$ where \$R_c\$ is the resistance of the transmission wires from which, we get \$P_c = \frac{P^2R}{V^2}\$

However, to me, this feels redundant, why can't we simply cancel out \$P_c\$ and \$P\$ and get back the standard formula for power?

In other words, why isn't \$P_c=P\$?

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  • \$\begingroup\$ If you lose all the power, you're not delivering any power. I'm not sure what the confusion is here. You realize the \$V\$ in deriving the losses is not equal to the \$V\$ seen by the load, right? \$\endgroup\$
    – Hearth
    Sep 17 at 3:36
  • \$\begingroup\$ Thanks for helping with the formatting! \$\endgroup\$ Sep 17 at 3:36
  • \$\begingroup\$ You appear to be used to MathJax on other sites, where $ is the escape character. For some reason, on this stackexchange, the escape character for inline equations is \$ (i.e., \$e = mc^2\$ for \$e = mc^2\$). $$ remains the escape sequence for 'full' equations. \$\endgroup\$
    – TimWescott
    Sep 17 at 3:36
  • \$\begingroup\$ @TimWescott, I see, thanks! \$\endgroup\$ Sep 17 at 3:37
  • \$\begingroup\$ @Hearth, unless I'm mistaken, that's what my textbook assumes while deriving the formula \$\endgroup\$ Sep 17 at 3:38

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