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I have seen when a capacitor is connected to a dc source it takes infinte time to charge, but when connected to ac it takes the potential of the source instantly,

probably the approach in the books is not adequate, please clarify,

Here is a link that mentions the time constant for DC https://www.electronics-tutorials.ws/accircuits/ac-capacitance.html

And here is one that describes the AC https://physicscatalyst.com/elecmagnetism/growth-and-delay-charge-R-C-circuit.php

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    $\begingroup$ Where have you seen this? It is simply not true, so you may need to be more specific with your references in order to receive a good answer. $\endgroup$
    – J. Murray
    Dec 24, 2020 at 3:17
  • $\begingroup$ when we connect a capacitor to an ac source,instantaneous voltage of capacitor = voltage of source = e0 sin wt,available in any book or link on alternating current with pure capacitor,thanks $\endgroup$
    – sachin
    Dec 24, 2020 at 3:24
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    $\begingroup$ @sachin When you are asked to provide a source then you should do so. It makes you seem evasive and dishonest. I looked at two “links on alternating current with pure capacitor” and didn’t see the comparison you described. In fact, neither even discussed a switched DC capacitor only circuit. $\endgroup$
    – Dale
    Dec 24, 2020 at 5:36
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    $\begingroup$ @Dale,m sorry for late response as there is a time difference,its india,pl go thru the below links,thanks.response of capacitor to dc electronics-tutorials.ws/accircuits/ac-capacitance.html response of capacitor to ac physicscatalyst.com/elecmagnetism/… $\endgroup$
    – sachin
    Dec 24, 2020 at 14:39
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    $\begingroup$ @sachin I think you'll find that in a DC circuit with no resistance, the capacitor charges instantly as well. The characteristic charging time - in both DC and AC - is given by $\tau=RC$. $\endgroup$
    – J. Murray
    Dec 24, 2020 at 14:50

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Regarding the transient currents (transient regime actually), it is there when you turn on an AC circuit that was off. I mean when you switch on the power. What you see in most description is the solution after the transients have "died" but the complete solution includes both. In most introductory physics we don't see this mentioned but electrical engineering books should have it. If you had AC circuit with very large inductance you could actually see the delay until the non-transient regime takes over.

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    $\begingroup$ I agree. Usually it is ignored but you can find the transients easily using the Laplace transform. $\endgroup$
    – Dale
    Dec 24, 2020 at 16:13
  • $\begingroup$ @nasu,what actually puzzles me is that the voltage is changing almost every instant in a contineous manner leaving no room for the transient currents to enter,i hope the sin graph is taking time to change for the capacitor to take the changes,hope the transient currents come in play not only in the beginning but comes whenever there is a change in voltage. $\endgroup$
    – sachin
    Dec 24, 2020 at 17:53
  • $\begingroup$ This is because you are looking the steady regime, after the transients have died. $\endgroup$
    – nasu
    Dec 24, 2020 at 22:08
  • $\begingroup$ @sachin, nasu hits the mark with this. At the heart of AC analysis is the stipulation that the circuit is in AC steady state, i.e., that transients have decayed to insignificance. Note that, even in a simple series RC circuit with AC voltage excitation, the capacitor never charges to the source voltage, i.e., the amplitude of the sinusoidal voltage across the capacitor is strictly less than the amplitude of the voltage source and, further, the difference is frequency dependent. This is why an RC circuit is a filter. Finally, there is a phase difference too. $\endgroup$ Dec 24, 2020 at 22:28
  • $\begingroup$ yes,seems its cleared,just one thing the current that flows thru the capacitor,what type of current it is,transient or something else. $\endgroup$
    – sachin
    Dec 25, 2020 at 12:15
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Capacitors always take time to charge. In practice, when a capacitors is ~99% charged , we can call it fully charged. The exponential which is used to describe the charging of a capacitors does not make sense when time is very large because charge can never be less than charge of an electron while in the exponential equation, for a large enough time you can get charge less than charge of an electron which is meaningless.

Having that said, the exponential is a very good approximation for short time. In AC (just like DC) the capacitors need some time to charge. It is this extra time that causes the voltage across them to lag behind.

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  • $\begingroup$ To be sure, an exponential doesn't necessarily describe the charging of capacitors. $\endgroup$ Dec 24, 2020 at 3:38
  • $\begingroup$ i just meant how the charging and discharging happening so fast as the ac frequency is as high as 50 or 60 hertz,does the capacitor ever get charged and discharged so fast,why transient currents are neglected,thanks. $\endgroup$
    – sachin
    Dec 24, 2020 at 14:24
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The site that you mention says

When a capacitor is connected across a DC supply voltage it charges up to the value of the applied voltage at a rate determined by its time constant.

However the time constant is $\tau = RC$ so it is not a property of the capacitor by itself, but rather the circuit.

Their example circuit for the AC case has a resistance of 0. So the time constant is $\tau=0$. Therefore it will instantaneously charge for both the AC and the DC cases.

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