I have a small battery bank used in my solar powered workshop anyway back to the question.I wanted to run some garden light from my power inverter about 200watts of lights what battery capacity would i need to run that for lets say 12hours
Not including inverter losses (on the order of 20% or so, you would need 240 AH of battery capacity. The additional capacity would be so that you do not fully discharge the battery and therefore damage it. Adding inverter losses and a factor for reserve capacity, your minimum consideration should be about 300 AH.
200 watts 120 volts x ? amps The current is 1.7 amps. ? amphours 1.7 x 120 The amphour capacity if the battery needs to be at least 200. That would only be true if the inverter was 100% efficient. They all produce heat and consume some energy. I'll speculate an 80% efficiency, requiring a 25% adjustment to 250 amphours. Unless you've an impressive array, you are likely asking too much of the solar panels.
To pull 200 W from a 12 V batttery for 12 h PU * I (Ohm's law) It will draw at the rate of 16 2/3 A Therefore you need to have a battery of 12 * 16.6666 * 12 2 400 Wh total capacity. Read the label on your battery. If it is a bank of several batteries, then the capacity it's the sum of all. Now, you should worry about how deep you are discharging your battery. A NiCad cell can go practically to zero and happily recharge again. Don't let it go absolutely flat, then it may re-charge with opposite polarity. (!) A Lead Acid cell (and most automotive types) will not recharge well if you discharge them more than about 40 % (of total rated capacity) - Yes, that is true, automotive batteries are not made to be discharged often. NiFe (Nickel-Ferrite) cells are very safe for repeated discharges too. (Mr. Thomas Alva Edison's contribution to the world) Most other cells in use today can be deep-discharged without ill effects.
