They are the exact same size and you can use them interchangeably. The diffence is that the 168 will be brighter than the 194. Although it is brighter, the 168 will not last as long (1500 hrs) as the 194 2500 hrs.
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The 168 has 3 candle power vs the 194 with 2. Since the 168 is slightly brighter it produces a bit more heat (3.8 vs 4.9 watts). In most situations where 194's are specified you should use an exact replacement to avoid heat damage from the hotter 168 bulb.
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Is the bulb burned out? Is the fuse for that side brake light good? If both answers are 'yes', then perhaps you should have an automotive electrical specialist check out the problem.
electricity because a light bulb needs electricity
If there is a bulb, it should work.
A: HARD TO SAY because a bulb has different resistance as it warms up
Exactly...you answered your own question. Each DC bulb will drop voltage according to its resistance and the amount of current it draws.