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A resistor obeys Ohm's law (\$\small V=I\cdot R\$); the current through it is equal to the voltage across it divided by the resistance (equivalently \$I=\frac{V}{R}\$).

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What's the purpose of these two diodes in this circuit?

Let's not forget the temperature dependency of the diode voltage. In this circuit the output current has an NTC, which could be important. A popular variant used to be to replace the 2 diodes with 1 …
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