I am planning on making a circuit similar to this:
Do I need a current limiting resistor to drive the LEDs if the solar cell is only providing 3v? Thank you so much for your help!
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3V is low enough that the resistance of the diodes is enough limit the current so they won't blow up immediately, but controlling the current is always a good idea. The voltage is so low, a simple current driver may be a better than a resistor:
The current trough the transistor (Ice) will be about 100x the current through the base (Ib). Keep in mind this about 0.7V across the base and emitter of the transistor, if you wanted to calculate a new R1, and the gain will increase (and try to drive more current) if you leave it in the sun. You just make R1 bigger if that's an issue.
It depends how many (m)A they can provide. The maximum for normal LEDs is around 40-50 mA so if the solar panel provides more the LED will be smoking.
You have to use the following formula:
V = I * R
V (voltage) is 3, however, you should reduce the forward voltage of the LED, which is normal 1.7 to even upto 3.5... So let's take a safe value of 1.7V.
That leaves 3 - 1.7 - 1.3 V (per 'chain')
I is 0.07 / 2 (chains ) = 0.035 A
So 1.3 = I * R <=> 1.3 = 0.035 * R <=> R = 1.3 / 0.035 = 37 ohm (for each resistor). If you don't have these, take the first higher value.
Best approach is to place 2 or more smaller solar cells in series and put the LEDs in series. Regulating current with tiny overhead voltages is difficult.