Can I safely charge capacitor 2.7 V 500 F with 12 volt car battery? Have tried with a 3 V charging adapter and 12 V light bulb as resistor but doesn't take charge. I didn't want to try 12 V in case it blows up.
It doesn't matter what voltage your power source is, as long as the capacitor is not subjected to a higher voltage than it is rated for.
You could, for example, charge the capacitor from a 12 V source with a resistance in series with it. That will start the capacitor charging exponentially towards 12 V. You have to monitor the capacitor voltage and disconnect it when it reaches its maximum allowed value of 2.7 V.
For example, let's say the capacitor starts out empty and that you are charging it from 12 V with 100 Ω in series. The 500 F capacitor and 100 Ω resistor have a time constant of 50,000 seconds, or 833 minutes. Going from 0 V to 2.7 V would take 0.25 time constants, or about 3.5 hours. The capacitance is probably not very accurate, so you don't just want to wait 3.5 hours and turn it off. After 3 hours, you should be monitoring the voltage carefully.
Another option is to put a 2.7 V shunt regulator across the capacitor. Using the above example, there will be (12 V - 2.7 V) = 9.3 V across the resistor when the cap is fully charged. That means 93 mA will be flowing thru the resistor. A shunt regulator that can handle 100 mA would work to limit the capacitor voltage safely, regardless of how long it is connected to the 12 V supply and resistor.
No. You cannot safely charge any capacitor that is rated for 2.7 V to any voltage higher than 2.7 V.
If you have previously charged it to 12 V, that might explain why it doesn't take charge now.
Charging it to 12 V through a resistor is still charging it to 12 V, which is 4.44 times the voltage that the capacitor is rated for.