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Diode is simply a one sided switch that allow to flow of current in only one direction with drop of some known voltage level. current flow will depend on the remaining circuitry.
However diode behavior is like a switch and current flow depend to other components in the circuit but diode needs to a minimum direct current and voltage for start and then the voltage of top and bottom of it (when it is on) will be 0.7 volt in silicon diode and ....
Reading the initial question strictly, when "applying a voltage", you'll observe a current according to the exponential diode characteristic. Review the data sheet of the respective diode to get the exact characteristic.
current in diode circuit, will depends upon the current limiting resistor value we put in series with diode.
let me explain you, what happens if no resistor, when supply voltage is greater than 0.7V, say 3.3 V, then internal resistance of diode which is very low in milliohms comes in to picture, and a current of value 3.3 (supply)-0.7(diode drop for silicon)/ x mohm = many amperes flows in circuit and your diode burns.
So to avoid this we put series resistor in place and it is called current limiting resistor (for its function).
consider an LED circuit.
normally a 15-20mA is a good current to pass in your LED circuit. So, resistor calculation is as followed:
drop across resistor: 3.3 - 1.5 (for LED) = 1.8
current = 20mA
value= 1.8 / 0.02 = 90 ohm
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