In essence, a failed (bad) capacitor appears as a "short" in the circuit, as opposed to a failed (open) resistor which appears as a "break". Unless of course the capacitor has exploded - in that case it'll probably be a "break" as well, but don't count on it.
It depends on the function of the capacitor. If the capacitor is used to 'smooth out' (filter) unfiltered voltage, this function will be lost and in addition, the capacitor will "load down" the voltage rail it's supposed to smooth out. If, on the other hand, the capacitor is part of an oscillator circuit (be it a standalone oscillator, an oscillator network, or timing source for an integrated circuit), the frequency of the oscillation will be greatly offset from the ideal value, and this may appear as many different problems (instability and lack of synchronisation with signals among others) which wouldn't easily be tracked down to the bad capacitor.
If, on the other hand, you were asking about what chemical and physical events take place within the capacitor as it fails, this question should be filed under "Chemistry" or "Physics" at least in additon to, if not in the stead of, "Circuits", and it would be wise to include a word or two asking about the reactions within the electrolyte itself (as most failed capacitors are electrolytic).
Too high of voltage, bad motor the capacitor is running , or power surge
when a capacitor reaches it, it acts as a battery
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What happens to the current in a circuit as a capacitor charges depends on the circuit. As a capacitor charges, the voltage drop across it increases. In a typical circuit with a constant voltage source and a resistor charging the capacitor, then the current in the circuit will decrease logarithmically over time as the capacitor charges, with the end result that the current is zero, and the voltage across the capacitor is the same as the voltage source.
If you apply a higher voltage to a capacitor than it is rated it could over heat and explode.
In order to double the voltage across a capacitor, you need to stuff twice as much charge into it.
As the capacitor charges the led will dim until it's minimum operational voltage is reached and it goes out.
There are two ways to read this: you have a burned-out run capacitor on your motor and a good start capacitor in your parts box, and you have a burned-out start capacitor and a good run capacitor. If the run capacitor's bad and you want to put the higher-voltage start cap in its place, the answer is yes. This is called derating, and the only thing it does for you is increases the lifespan of the capacitor because you're not working it as hard as it can take. If the start capacitor's bad, don't do this--they used a 440-volt capacitor in there for a reason.
An inductor can be used, in principle, but it has to be the right inductance, it will waste more power than a capacitor, and the motor would rotate the opposite way.
Yes, a bad capacitor causes blower motor to become slow or stop. Since bad or shortcapacitor will make the surge of current and tripping of circuit breaker.
Bad bearings, shorted or open windings and perhaps a bad starting capacitor.
An open circuit, by definition, has no continuity, therefore there is no current flow. A failed capacitor in an open circuit would have absolutely no effect.