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Current limit of TO220 LM317 is above 1.5A

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The IC has internal over-current protection. Rated maximum load current is 1.5A minimum, 2.2A typical, but no higher figure is given. It's probable/possible that the over-current protection would kick in before 3A, even for a short overload period.
A well-designed circuit would not have components operating at or very close to their rated limits.
 
Thanks, the datasheet is unusual, because page 13, fig 17, suggests that the LM317 can carry 1.25V/0.2R = 6.25A.
Yes, that's an error in that data sheet..
The LM317 output current is indeed internally limited to 1.5A (min).

If you need more you can increase the current as shown by Figures 22 and 23 in the data sheet.
 
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