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sram

The capacitor

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Hello there! Read this statement:

A capacitor is a reactance that changes with time.

How true or false is this??

I just wanna show your comments to one instructor because i'm in disagreement with him :D

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Hello there! Read this statement:

A capacitor is a reactance that changes with time.

How true or false is this??

I just wanna show your comments to one instructor because i'm in disagreement with him :D

Disclaimer: I havent been doing electrodynamic stuff for years, and my english terminology for it is a bit weak...

Yes, its true. In two different ways, depending on what general assumptions you base the argument.

A capacitor _has_ a reactance. Which is depending on the frequency composition of the input signal. So in a general case (i.e. a non-periodic input funtion), the resulting imaginary resistance is time depending.

So in this case, the statement is true.

Also, even with an ideal periodic function (only one frequency component), the statement can be considered true if you take into account the complex character of the resistances involved (rotating in the complex plane).

Edited by imsabbel

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You are thinking too much imsabbel. Take it that this is an introductory course. we are talking about the periodic AC source. students don't know what imaginary numbers are.

The instructor put this statement in a test and it was a true or false question! I put false of course and I was marked wrong..........!!

His reasoning:

Xc= 1/2pi*f*c

and since f= 1/T then Xc changes with time!!

I told him this is wrong because BIG T is defined to be the period it takes the signal to complete one cycle. It is not small t we see in the AC graph.

I know what he means but he didn't know how to ask the question. You need to be really precise with such questions. He should say changes with frequency ......................or at least periodic time(although I don't like it this way either). You change the frequency in an AC source. You don't say I will change big T.

His statement clearly implies that Xc changes as time passes, and this is of course is incorrect.

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His reasoning:

Xc= 1/2pi*f*c

and since f= 1/T then Xc changes with time!!

I told him this is wrong because BIG T is defined to be the period it takes the signal to complete one cycle. It is not small t we see in the AC graph.

I think maybe your instructor's question wasn't necessarily appropriate for an introductory course, though he is probably right.

Consider this: The reactance of a capacitor is the ratio of the voltage to the current (Xc=Vc/Ic). So can you think of it this way: in an ac circuit, when the voltage of a capacitor (across the two plates) is zero, the current is maximum; and when the voltage of a capacitor is maximum, the current is zero:

http://www.st-andrews.ac.uk/~jcgl/Scots_Gu...plex/react.html

Since the current Ic through a capacitor leads the applied voltage Vc by 90 degrees, isn't the (instantaneous) reactance then always changing? Someone said that electrical resistance is like friction, while reactance is like energy storage (if mechanical analogies help) so consider how a capacitor charges and discharges in various degrees when an ac signal is applied. I never did quite understand the imaginary aspects of impedance, though I'd bet that comes into play too, like imsabbel said.

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You are thinking too much imsabbel. Take it that this is an introductory course. we are talking about the periodic AC source. students don't know what imaginary numbers are.

The instructor put this statement in a test and it was a true or false question! I put false of course and I was marked wrong..........!!

His reasoning:

Xc= 1/2pi*f*c

and since f= 1/T then Xc changes with time!!

I see.

Well, in this case, the instructor is wrong.

Could it be that with "time" he means "cylce time" or some other engineer lingo?

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I'm actually an electronic engineer, so this is in no way tough for me. I had to take this introductory course at work. (refreshing and all those who work in my place should take it)

We studied DC and AC, and we studied some CKT components(R, L, C, diode, transistor.............etc)

We took the Xc formula and I knew how far I should think. He wanted to ask whether C reactance changes with frequency, but didn't know how to ask the question.

>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>reactance of a capacitor is the ratio of the voltage to the current (Xc=Vc/Ic). So can you think of it this way: in an ac circuit, when the voltage of a capacitor (across the two plates) is zero, the current is maximum; and when the voltage of a capacitor is maximum, the current is zero:

http://www.st-andrews.ac.uk/~jcgl/Scots_Gu...plex/react.html

Since the current Ic through a capacitor leads the applied voltage Vc by 90 degrees, isn't the (instantaneous) reactance then always changing? Someone said that electrical resistance is like friction, while reactance is like energy storage (if mechanical analogies help) so consider how a capacitor charges and discharges in various degrees when an ac signal is applied. I never did quite understand the imaginary aspects of impedance, though I'd bet that comes into play too, like imsabbel said>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>

I should not think this far!

Edited by sram

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True enough for a flux capacitor at least.

Changes with time is correct, though not necessarily changes with frequency since the reactance is changing within the AC cycle. Reactance will be lowest near the AC peaks and troughs and highest when voltage is changing quickly in between.

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A capacitor is a reactance that changes with time.

How true or false is this??

Well it's a stupid question but false would be the best answer.

The most general behaviour of a capacitor is defined by i = c dv/dt

For steady-state sinusoidal signals this gives |I| = 2 Pi f c |V|, or |V| = X_c |I|

where the reactance is given by X_c = 1/(2 Pi f c).

So the reactance is only time varying if either

1. The capacitance itself is time varying, or

2. The frequency is time varying.

Referring to 1. There is nothing to stop one from building a capacitor whose capacitance value can be varied with time, but certainly you should assume that the capacitance is a constant unless otherwise specified, particularly in an introductory course.

As for 2. Strictly speaking the concept of steady-state sinusoidal analysis implies that the frequency is constant. In practice however if the frequency is varied slowly enough then you can maintain what's often referred to as a "quasi steady-state", where the concept of a time varying frequency is somewhat useful.

In any case the original statement is false and the reasoning given (since f= 1/T then Xc changes with time) is utter nonsense.

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True enough for a flux capacitor at least.

Reactance will be lowest near the AC peaks and troughs and highest when voltage is changing quickly in between.

Complete nonsense. Reactance is defined as the ratio of quantities of steady state sinusoids (ratios of RMS values or ratios of amplitudes). Reactance is NOT defined in terms of instantaneous v and i values.

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V lags I. Meaning, volt is delayed by 90 deg by I which takes current to charge up that cap to see voltage rise. So voltage rises and falls by 90 degrees.

BTW, capacitor DOES not pass current. It is used to isolate two circuits (used in signal transfer) and to buffer & smooth voltage that circuit requiries.

Also there is other circuits that uses the C constant of a cap to generate sawtooth of some types. As well as paraola waveform ampified from very weak ripple off a capacitor of low frequency for example to shape the high freq component (ie pincushion).

When you have to fix, much of circuits depends on ESR of electrolytics. Once ESR is too high, circuit operates irratically or stop working, or worse blown up. So get a bob parker's ESR meter for this.

Cheers, Wizard

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A capacitor is a reactance that changes with time.

How true or false is this??

Well it's a stupid question but false would be the best answer.

The most general behaviour of a capacitor is defined by i = c dv/dt

For steady-state sinusoidal signals this gives |I| = 2 Pi f c |V|, or |V| = X_c |I|

where the reactance is given by X_c = 1/(2 Pi f c).

So the reactance is only time varying if either

1. The capacitance itself is time varying, or

2. The frequency is time varying.

Referring to 1. There is nothing to stop one from building a capacitor whose capacitance value can be varied with time, but certainly you should assume that the capacitance is a constant unless otherwise specified, particularly in an introductory course.

As for 2. Strictly speaking the concept of steady-state sinusoidal analysis implies that the frequency is constant. In practice however if the frequency is varied slowly enough then you can maintain what's often referred to as a "quasi steady-state", where the concept of a time varying frequency is somewhat useful.

In any case the original statement is false and the reasoning given (since f= 1/T then Xc changes with time) is utter nonsense.

My thoughts almost exactly!

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