why isn't $P=P_c$ where $P$ is the power that we want to supply and $P_c$ is the power lost during transmission

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\$$?

• 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? Sep 17 at 3:36
• Thanks for helping with the formatting! Sep 17 at 3:36
• 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. Sep 17 at 3:36
• @TimWescott, I see, thanks! Sep 17 at 3:37
• @Hearth, unless I'm mistaken, that's what my textbook assumes while deriving the formula Sep 17 at 3:38