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The datasheet for the LM358 states that it typically sources 20mA. Lets say I want to power a single LED on the output.
Do I have to put a resistor inline or since it can only source 20mA I'm good?
It depends on the output impedance of the IC in question axro. Somewhere in the datasheet it should tell you the conditions under which you can get 20ma out or otherwise specifically state the output impedance, regardless of the device you're going to need a current limit resistor, an LED will try to draw more than the 20ma that the IC is rated for and could damage the I/O line by trying to draw more than it's rated for. In general it's a good bet to assume the output impedance of any cmos based device is very low even if it can't provide a lot of current. The current limit is the physical limitation of the size of the output drivers.
A red LED is 1.8V to 2.0V. A blue or white LED is 3.5V.Do you need to cut it that close?
My databook says 2 volts at 20 ma. Allow another 1.8 or so for the led.
Not if the opamp has a max output of only 10mA, then its output resistance is (15V - 2V)/10mA= 1.3k ohms. If you add 750 ohms in series then the current is (15V - 2V)/750 ohms + 1.3k ohms= only 6mA.Put a 750 ohm in series and have at least 15 ma. (assumes a 15 volt supply)