Some capacitors are polarity sensitive; some are not. It depends on the design. Electrolytic capacitors, for instance, are polarity sensitive, while ceramic disc capacitors are not. You can generally tell, if the capacitor is marked with polarity signs, such as + and -, if it is or not.
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For electrolytic capacitors, yes, as ignoring their polarity can damage them.
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The electrolytic capacitor can only have voltage across it in one direction. Failure to comply will result in catastrophic destruction of the capacitor.
To determine polarity in CAPACITORS:Electrolytic capacitors are often marked with a stripe. That stripe indicates the NEGATIVE lead.If it's an axial leaded capacitor (leads come out of opposite ends of the capacitor), the stripe may be accompanied by an arrow that points to the negative lead.Sometimes, you can look to the length of the leads as an indication of polarity. The positive lead is usually longer but be careful if you're reusing old or 2nd hand capacitors - the leads may have been trimmed.Tantalum capacitors are often marked with a '+'sign.http://www.westfloridacomponents.com/polarity.html