I'm starting with electronics and I don't have a lot of resistors. Every new project I try to do, I have to buy new resistors, but they take a long time to arrive.
What's the solution? What variable resistors should I buy?
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There is a thing named resistance decade. It is like a programmable resistor, you can set the value and it precisely holds it. Costs about 100 to 1000 USD depending on precision and wattage.
Other cheaper solution is to buy a Resistor Assortment Kit. It includes 20-50 pcs of every value of resistors. You can find it on ebay from 10 USD
Another idea is to just buy resistors.
I buy resistors in packs of 100 for about 50p each; packs of 1,000 are also available for £2.88 each. They are 1/4W, 5%, carbon film.
First, I'd recommend you stock up on the most common values: 10, 47, 100, 470, 1k, 4.7k, 10k, 47k and 100k provide a good range. Then get the in-between values. You'll rarely find a use for 1M+ resistors, so I don't have any of them.
I would recommend getting an assortment of some kind from your electronics dealer, they should have some. You'll probably get them cheaper that way, too. If you do SMD, you might need separate sets for different sizes plus a pth kit. But the price still isn't bad and usually those kits are so big you won't have to worry about it after you buy one set. If you find yourself running out of one size (220Ω, 10kΩ), you can get a strip/tape of 100(0) and be set for a long while again.
In many cases you can get away with rounding the values a lot, so you'll probably only need a few per magnitude. You can combine values and a few pots/trimmers can help test values quickly (while prototyping).
That decade box (or such) can be made if you can find the switches. There should be ready schematics for various types.
Either way, I'd say stock up on a wide set of values. If you're doing anything more than putting together a ready kit now and then, you can probably use the selection. There's also a couple of other questions here about how to keep those parts in order, what parts to keep in stock, and what belongs into a "basic electronics kit".
One option is to combine resistors in series and parallel to produce the resistance you need.
Sometimes you can use a good emulator like qucs, that is free.