When women begin taking birth control pills it takes at least thirty days to begin working, but you should probably give it sixty days, just to be safe.
If you switch pill brands you should consult your doctor on the specific pills you're using and how their combination works. If the two are similar then you may be able to pick up where you left off (that is to say you'll still be protected), but if they are significantly different, the new one may not kick in for the standard thirty days or longer.
For more information on birth control pills, check this link out.
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