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Rectifiers don't "stabilize the output voltage" of rectifier circuits when input voltage fluctuates. The rectifiers just rectify the input, and the output will fluctuate as the input does. Another form of "conditioning" of the rectified output is needed to address the issue of fluctuations. And we use the term regulation to talk about the effect of "stabilizing" an output voltage. Through regulation, the output will be resistant to changes in voltage when changes in the input voltage occur.

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Q: How do rectifier circuits stabilize the output voltage when the input voltage is subject to fluctuations?
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