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Can someone help me to identify this component marked "10mΩJ?" I'm pretty sure it's a 10 mega ohm resistor, but I can't find it anywhere to buy one. Maybe a similar resistor can work, but I don't have more information, like type and how much it can handle since it is for a ballast (car light control circuit.)
It is a 0.01\$\Omega\$ (10m\$\Omega\$) resistor with tolerance +/-5% (J).
Chances are pretty good that if it's burned up then something else (such as a semiconductor) is kaput as well.
'm' for milli, 'M' for mega.
If it's for a lighting circuit it might be a current shunt and so 10 mΩ (0.01 Ω) would make sense. The controller will monitor the voltage drop across the shunt and use that to determine whether the light is off, on or short-circuited. From Ohm's law you can calculate the voltage drop per ampere of current through the lamps, \$ V = IR = I \times 0.01 \$ so 1 A would give a signal of 10 mV.
'J' may be a tolerance. In the SI system of units it is the symbol for 'joule', the unit of energy. This is unlikely to be its purpose on this marking.
