For that 20 ma you need a 500 ohm resistor.
0 5 volt led.
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But using the joule thief it works like a charm.
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Not only does it work with a brand new battery but it works until the battery is nearly dead down to 0 3 v.
A wide variety of 0 5 volt led light bulbs options are available to you such as e27 e17.
Always use a series resistor.
But a 1 5 v battery like a aa cell simply will not work.
Almost all common leds are not.
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The blue led has a typical forward voltage drop of 3 2 v therefore a 5 ω resistor is required when using a 3 3 v supply voltage.
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If you make 20 ma flow at 13 v then at 5 v the led will still work but at a lower brightness.
Never ever connect a led directly to a supply unless it is specifically designed for that.
Normally if you want to light up a blue or white led you need to provide it with 3 3 5 v like from a 3 v lithium coin cell.
500 ohm resistors are hard to find so get some 560 ohm resistors that s close enough and use one.