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When you first turn on your DC circuit, you are going from zero volts to something volts (lets just say ten) so this is sort of like an AC voltage because it takes time to rise to 10 volts. as such, the capacitor looks sort of like a short circuit the instant we turn on power. Then, the capacitor will charge and after five time constants (One time constant being R x C)

E.G. if you have a 1k resistor and a 10uF capacitor, one time constant would be

1000 x 0.00001 = 10mS

therefore your capacitor will be charged after 50mS

as for using a capacitor in an AC circuit, the capacitive reactance (which is like resistance) will vary with frequency and also the value of capacitor.

It is found by the formula

1/(2πfc)

so if we had an ac frequency of 1KHz and a 10uF capacitor then the 'resistance' (correctly termed reactance) of the capacitor is:

1/( 2 x π x 1000 x 0.00001) = 15.9 ohms

So in this case, it is quite close to being a short circuit.