Difficult one. Looks like it has yellow and purple so a multiple of 47.This looks like a board from a battery charger of some kind, would I be right? If so it could be 4.7 ohms or 47 ohms. Based on similar experiences I have had I would say 47 ohms. If I am correct, the thing to do is tailor the resistance to the battery is is charging. If it's (say) a 1 amp hour battery, tailor the resistance so that it charges at around 100mA (1/10 of the battery capacity) maximum.I'll take another punt here, it's a charger for a NiCd (Nickel Cadmium) or NiMH Nickel Metal Hydride) battery (now obsoleted by Lithium batteries). You would often find chargers advertised as "Fast Chargers" with the ominous warning in the instructions "DO NOT Charge for more than 5 hours". They were just a resistor, like this, and if you left the battery in for over that time the battery would be cactus. Don't jsut replace it, change the resistor so it's charging at 1/10 the battery capacity and it won't matter if you leave it on for a day or longer.A possible reason for the resistor's demise is that one or more cells in the battery have shorted, so the resistor has to drop more than the usual voltage. Check the battery - you should have more than 0.5V per cell if they are good. Any that are not, give them (single cell only)a zap or two with a high current 12V source (eg a car battery) with a 20-50 watt headlamp bulb in series - this will run a current of 2-5A through the battery and burn off the cadmium whiskers that cause this short-circuting. After you've done this the battery should read above 1.2V (put a meter across it while you do this if you can).Some time ago I designed a circuit to do this repeatedly - zap the cell with 3x capacity for 10 seconds, then discharge it to 1.1V, then zap again. Half an hour of this and the cell would be ready for another yar's work normally.If this was not from a battery charger, let me know what it IS from and I'll make some more educated guesses!