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Everyone knows how to calculate the resistance of a current limiting resistor for a LED but is it possible to go the other way? (aka determine the supply voltage from the resistor's value)

I ask this because I am working on re-purposing ink jet printer parts for low cost 3D printers to be built in developing countries. Ink jet printers used to use stepper motors but recently have started using DC motors with optical quadrature encoders. In order to use the e-waste one must find the voltage at which the quadrature encoders are supposed to operate at. While the forward voltage of the LED isn't known, is it possible to determine a ballpark idea of what voltage should be used to power the LED in the quadrature encoder?

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    \$\begingroup\$ I'd be interested to know a bit more about your end use situation. I have interest in other developing country applications. My contact email address is on my profile page. \$\endgroup\$ – Russell McMahon Jun 18 '15 at 8:51
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Sorry, but no. Attempting to drive an LED with a constant voltage is a great way to kill an LED. The coefficient of forward voltage with temperature is negative, which means that, driven by a constant voltage, if the LED starts to get warm it will start to draw more current, which will increase the power dissipated by the LED, which will cause the forward voltage to drop even more, etc to disaster.

You are better off assuming an LED forward voltage of about 2 volts, then provide a convenient voltage/resistor combination to provide ~ 1 mA, then measure Vf. Then reduce the resistance so as to produce a series of currents in the 1-10 mA range, and at each current setting check the encoder for proper operation.

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Check for part numbers on the detectors, they are likely to be HP/Agilent units.

If they have built in resistors they will probably work on 5 or 3.3V if they use external resistors power up the printer before parting it and measure the voltage at the detector and before the resistor connecting to the LED if you can find it.

To calculate the third value of current, voltage and resistance you need the other two.

I would assume 5V or 3.3V in modern printers, 5V or 12V in older units. Check the PSU voltage rails and see if there is some strange 7 or 9V rails, suspect those if other calculations do not pan out though they are more likely used for the head or motors that cannot be accommodated from a standard rail with a resistor change.

EDIT:
As mentioned there are pretty standard voltages for LEDs. usually 1.7 to 1.9V for IR leds. Current for a sensor LED is likely to be in the range of 1 to 20 mA

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