ah yes, I understand now The current takes the path of least resistance and because the short has a resistance of 0 Ω, there will be no current through the capacitor. Thank youGo ahead and don't ignore the capacitor and do the current division between it and a 0 Ω short and see how much of the current goes through the capacitor. Then reflect on why it is what it is and then see if the shortcut of ignoring it during the analysis makes sense. I suspect it will be a useful exercise for you because you are inquisitive enough to be asking the question in the first place.
As a complete aside, is the solution you posted from the text? If so, could you do me a favor and look in the first chapter or so of the book and see what the author says about units? I suspect that they will say something about how units are really important; most textbooks do give some kind of lip service to units even though, as demonstrated here, they don't really mean it and will just tack onto their answer whatever units they want or expect.
I can't help but wonder how many millions of man-hours of effort have been wasted, not to mention millions of dollars of equipment damaged or destroyed, or the number of people injured or killed because these textbook authors, the majority of whom have little to no experience outside of academia, show by their example that tracking units is beneath them regardless of whatever pronouncements they tout in the first chapter.Yes, it's part of the solution manual of the textbook (Fundamentals of Electric Circuits, Alexander; Sadiku; 6th ed).
And as you suspected, chapter 1 of the book is about the units and about how important they are. But even in exercises from this chapter they just add the units they expect/want at the end
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