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You can measure the current generated with the digital volt meter even if you get "0.000" when the meter is set to current mode. You just need to know what the input impedance of the meter is in voltage measuring mode. (You can use a second meter to measure the input resistance (impedance) of the first, or you can find the value in the meter's manual.) Digital meter are often either 1 or 10 Megaohms input impedance. Using Ohm's law you have Current=Voltage/Resistance. A 10 megaohm meter that reads 0.01 volts means the LED is generating 0.01Volt/10^7 Ohms = 10^-9 amps (1 nanoamp). The power generated (or consumed) in a DC circuit is just voltage times current so the LED is generating about 10^-9 Amps * 0.01 Volts = 10^-11 Watts (10 picowatts).
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