Which Resistor To Choose And Why

How can I choose the right spark plugs resistor to any car?

Generic spark plugs are basically universal for any gas engine. Diesel engines don’t have spark plugs - so not any car.High performance engines would require spark plugs that can handle higher application.

What resistor should I have for a 3mm LR LED?

There is an important detail that has not been mentioned yet.  But first I will explain why you need a resistor.An LED, or any diode, has an exponential current-voltage relationship.  This means that for a change in voltage, the change in current increases a lot as you get more positive.  LEDs generally have a turn on voltage of 2v, which means that at this point, there is noticeable amount of current running through th LED.  If you hook up an LED to a 5v supply (bench or wall supply, NOT the attiny or any mcu) without a resistor, the diode will allow a very large amount of current to flow, until the wires inside heat up and break.We don't want this, so we use a series resistor, which has a linear current-voltage relationship.  You choose the resistor so a desired amount of current flows, around 15mA, and there is an appropriate voltage drop of about 2v across the LED.  To size the resistor:R = (supply voltage - LED voltage)/LED currentYour LED doesn't have a datasheet, so these are approximate numbers:Supply voltage: 5vLED voltage: 1.8v (typical for red or ir LED)LED current: 10mA or 0.010AR =   (5-1.8)/0.01= 320 ohmsWe typically use 470 ohms for 5v supply and 330 ohms for 3.3v supply, so feel free to experiment by going higher than 330 ohms (but not lower)Are you wondering why I picked 10mA?  This is a detail many people are unaware of.  If you look in the DC electrical characteristics part of the attiny85 data-sheet, you will find a note (summarized here): Tests of pin output current were conducted at 5mA and 10mA.  A single pin can source more than this, but the total output current and through all pins must not exceed 60mA.  Basically, I chose 10mA since that is the recommended maximum output current for the pin.  You may be able to go higher, but not over 20mA.  And, if you have multiple LEDs sourced by the attiny, in total they cannot draw more than 60mA.  If you need more current, you would need to drive the LED using a mosfet or bjt transistor.  A mosfet such as the 2n7000 can switch about 250mA, and the attiny would only have to output nanoamps or smaller in DC.  If you need more brightness in the LED, that is your solution.  There are many good tutorials, just search "driving LED with mosfet".  Quick note about testing: the human eye can't see ir light, but some cellphones can.  If your cellphone doesn't have an IR filter, you will see a purple glow inside the LED.

Why does current choose the shortest path? Why doesn't it choose the longest path to flow?

It's more like "Electricity tries to follow the path of least resistance". The sentence is a non-rigorous intuitive tool that helps one quickly make sense of current paths. It's not a physical law.This comes from the behavior of resistors in parallel --this is where current has a "choice" of which direction to take. The potential difference across a resistor is equal to the current into its resistance (V=IR[math]V=IR[/math], usually called Ohm's law) in appropriate units.What happens when you have two resistors in parallel is that the p.d. across them must be the same. Which means that I1R1=I2R2[math]I1R1=I2R2[/math]. So, more current flows through the resistor with less resistance and vice versa. Current still flows through the greater resistance.So most current flows through the path of least resistance. In the case of a short circuit, one of the Rs is (nearly) zero, and thus (almost) all the current flows through it.

How do you choose the load resistor in a common emitter amplifier?

The emitter resistor affects no less thanQuiescent base current,Quiescent collector current,Voltage gain,Gain stability, andInput impedance (and the frequency response for AC amplifiers).Indirectly, the emitter resistance also impacts the usable values for collector resistance, which in turn affects output impedance, limiting the effective stage gain because of loading by the external circuit.Therefore it’s simply a matter of writing down these equations and selecting a resistance (or, more likely, a range of resistances) that satisfies all of the equations.Of course, this really amounts to solving several simultaneous equations, something most of us don’t cherish. This is why circuit simulator programs are so popular, but it’s still helpful to do these equations manually until you develop your own shortcuts.

How do I choose the value and wattage of dropping resistors when matching a power supply with a musical instrument amplifier design?

A Tricky question that really becomes "how do I design a power supply?"At a high level, the answer is, design a set of RC filters in your power supply to provide the voltage and current required by each stage of the amplifier.For instance, Say you want to build a little push pull EL84 amp. You know the power tubes will require 300VDC at 90mA to make about 16 or 17 watts with a Vox or Fender Deluxe style output transformer.Say you also want a cathode follower before the EQ and a long tail phase inverter plus a couple of stages of preamplification. If you use 12V dual triodes, they will want something under 200VDC generally at 1 - 9 mA.So, we grab a power transformer that puts out 260 VAC at 150mA. Off load, that is about 273 volts. For low cost, we connect the transformer to a full wave rectifier made up of 1N4007 diodes. For the first filter, if we had no resistor (or coil) the voltage would be over our desired 300VDC B+, so we'll add a 120 ohm resistor with a 40uf electrolytic filter cap to make an RC filter for B+. Smoothing is adequate and the slower filter cap recovery through the resistor mimics a tube rectifier and gives a little sag and bloom. I suggest using a big 10W resistor here for good heat management.Next, we build an RC filter of a 5W 6.8k ohm resistor and a 20uf cap. The output at this filter is firm 190 VDC and can provide 8-15mA for a 12AT7 for a phase inverter or tremolo stage.Next we make a filter from a 2 or 5W 10k ohm resistor and a 10 or 20uf cap. The output here is 180ish volts at low current, suitable for a couple of 12AX7 preamp tubes.Finally,  use a "drain" resistor of 2W 150k ohms at the end of the power supply, between rail and ground to make the power supply more consistent under changing loads and to drain those dangerous filter caps when the power is shut off.So, a general answer is, as little resistance as possible at the B+ stage of the power supply where the specs of the power transformer are suited to the power tubes, so they can draw full amount of current required, then higher resistances are used to drop the supply to levels safe for preamp tubes.

How do I choose resistors for a voltage divider? For ex: I want to reduce a 10V to 3V, 3k - 7k should be okay but there is no 7k available in digikey. Is there any table of resistors that gives various proportions with frequently available resistor values?

There's an E96 table that gives the standard values for resistors of 1% tolerance (space2 about 2% from each other. This repeats every decade so when it show 274 as a value that means you can get 2.74 ohm, 27.4 ohms, 274 ohms, 2.74K,  27.4K, 274K, etc.Resistor Values E6 E12 E24 E48 E96 E192Using E96 resistor values you should be able to get within ~1% of the ratio you want and the tolerance will be +/-1% of that.These tables (also in the link) provide spaced values at different tolerances. E12   10% toleranceE24     5% toleranceE48     2% toleranceE96     1% toleranceE192   0.5, 0.25, 0.1% and higher tolerancesYou will find 3.01K+/-1% and 6.98K +/-1% are standard values easily available. With a 10.000V source will give you 3.013 (about .3% high) volts if the resistors have no error. The possible range will be 3.05V  to 2.97V  (1.6% high to 1% low) with the standard values. assuming the 10.000V has not tolerance.If you need it closer you can go with tighter tolerance resistors (but will not always be readily available) or a trimpot or trim your reference 10.000 v.