I think it would actually be easier to wow people than people think. You'd just have to focus on older technology rather than completely modern stuff. If you know that steam engines are a thing, and even vaguely how they work, you can build the king a pump to get running water without having to run massive aqueducts, or a crane to build his massive projects, or any number of directly useful things. An understanding of basic germ theory could set you up to be the best doctor in the world. Or even just a bicycle would probably be quite useful to get around without a horse, and I'm sure anyone could make a rough mockup of a bike.
I think you underestimate what it takes to get modern plumbing water tight and easy to manage. Threading, clean threading, teflon, and easy to manage plastic pipes, have all been invented within the last 200 years. Mostly, the last 80.
and that's just the literal direct infrastructure within a house. Water towers are not simple. Underground pipes are not simple. Civil plumbing and waste management is not simple.
Nah, problems arise much earlier. Metals are expensive (proper steel is a thing of the 1700s, try getting proper coke) and your claims might be considered too outlandish for funding of home industrialisation, even making the needed tools might take ages.
Depending on when you are, science might even be considered evil, useless, unless you have very clear, direct and easy use cases (e.g. horse collar, compass, wheelbarrow).
Interesting could be the printing press for problem solving.
Proving electricity is easy, since even static electricity is relatively unexplained for a long time. You already know that metals are great conductors, hell, even what conductance roughly is. You know lead acid batteries. Simple conceptual motor and lead acid batteries together with printing press is probably enough to industrialise many societies early.
Actually, I think you just got what you should make first - a simple Gutenberg press. You could probably make it all the way back in the Bronze age, using copper or brass for the stamps and the rest is just wood and rope. You'd just need a basic knowledge of levers and screws, and suddenly you have (relatively) mass-production media.
And you need knowledge of the local language they might not even have a written form yet. No point in a printing press when you don’t have symbols to print.
Efficiency would certainly be pretty rough but wire's been around since about 2,800 BC. Copper would be the way to go if you could manage it but any conductive metal would get the job done to some extent.
Finding a reasonable safe insulator might be a little bit of a chore.
Soft metal bushings have also been around for a really long time.
Efficiency on magnets would be difficult, You might want to just use a really huge battery pile and electromagnets.
The manufacturing tolerances for the axle the wire and everything would be a fight.
I don't think you have a chance in hell of producing anything in the same efficiency range is what we have today, but compared to not having electricity at all... It might be worthwhile.
The thing is even if you make the electricity what the hell are you going to use it for? For light bulbs are going to need glass blowing in inert gases. You're going to need diodes resistors capacitors and transistors to do radio, You could probably usher in tubes but that shi*'s almost black magic as it is.
Copper is the easy part. Get it hot enough and you'll end up with high quality copper.. Sourcing the copper is much more difficult.
Finding magnets is somewhat simple, you just need some iron... That's a lot more difficult. Iron smelting is way harder than copper smelting (especially without electricity).
Making bearings is also difficult. It requires not only iron smelting but also high precision machining.
and that’s just the literal direct infrastructure within a house. Water towers are not simple. Underground pipes are not simple. Civil plumbing and waste management is not simple.
The romans did manage to build a nice system, tho. I hear the persians also managed one.
But it doesn't have to be up to modern standards, and certainly doesn't have to be with modern materials. Get the local cooper to make your pipes and reservoir with pitch-sealed wood. Or make it out of stone, or cast copper, or whatever they use to store water anyway. If it's Roman or post-Roman, they've already had some experience with running water anyway, that wouldn't be the impressive bit.
Threading and such is mostly useful for mass-manufacturing standard pipes and using it everywhere, but at least at first you'd just be doing it for a rich/powerful person or two, where you could do something labour-intensive and unscalable.
I'm not saying that you would get a perfect, modern system straight away, but if you can convince the people to give you the benefit of the doubt through a prototype or two, you could make something that works well enough. That would be what I'd be concerned about, even if you can magic away the language barrier, they'd likely just think you're mad.
Language isn't too much of a problem depending on the region. Assuming this is Rome or shortly before, Koine Greek and Latin are well enough known that you can learn it after a few years of study if you're good with languages.
Yeah, but I'm assuming you just get dumped there with minimal preparation. Otherwise you could also study up on early technology and know exactly what to make and how to make it to be impressive. And the 'convincing them you're not mad' problem still exists.
If you know that you get dropped in 14th Century England you could also prep and study Middle English since the Canterbury Tales is the first book written in that language. And we still have surviving copies.
You don't need to be super accurate for a basic pump. If you know the design you can get medieval blacksmiths to make the parts for you with close enough accuracy.
Steam engines are more complicated than people seem to think. There’s more to it than just boiling some water and voila! They’re pretty much useless without a governor. How many people know how to make this crucial component?