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3) Resistors and Power Considerations

My question as I was learning this stuff:1k 1/4watt through hole resistors
Ok, so, any type or resistance is readily available from 0.1ohms to 100megaohms can I practically use anything?

The answer is: Yes and no... Yes you are allowed to use any resistor but no you can't just use any resistor! Resistors must be sized to handle the power that will go through them or they WILL burn out and sometimes literally catch on fire(fuses don't protect circuits, they are too slow for this, fuses are only there to prevent fires). 

When you buy a resistor, from (sponsors welcome), you buy a specific value of resistance and power handling. Typical "through hole" (the ones with solid wire on either end) are 1/4Watt.

Solve for R to limit the circuit to 100mA
Design Example: 
An LED (Light Emitting Diode) Calls for a maximum of 100mA(same as 0.1A) current and the circuit will be powered from a 12V battery. Calculate the value and type of resistor to use If the LED has Threshold Voltage(forward voltage) of 3v.

Re-phrased from definition: Two steps to determine, 1) The value to "limit the current flow" to 100mA 2) The required power handling of the resistor. 

Background on LED: A diode is a "non-linear" device that has properties, due to semiconductor devices physics, that extend beyond  ohms law that determine the voltage drop across it.  For this LED the problem says the voltage will be 3V which is typical of a high power LED. The LED is treated as a second battery or fixed voltage point putting 12V from the battery - 3V from the LED turn on(forward voltage) leaving 9 Volts across the resistor. 

Ok, so, we are going to use the 9 volts calculated from the voltage sources in the problem for the Voltage = Current x Resistance => 9 volts = 100mA(max) x Resistor

Solve for equation:
9V/0.1A = 90Ohms Resistor Value.

Next practical step is to find a resistor in your toolkit that is somewhere in this neighborhood. 

What power handling class of resistor (1/4W, 1/2W, etc) is needed: Power = Voltage x Current
We could have calculated the power without knowing the resistor value... But with the resistor value we can calculate the Power in 3 different ways and verify that the equation holds.

Power(Watts) = 9 volts x 100mA = 0.9Watts. 

This means you will need at least a 1 Watt resistor for this circuit.

Question: When does this voltage thing happen when the voltage across the resistor isn't the battery voltage? Any time you are working with an LED, but voltage division is covered (insert link!)
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