The question asked on my quiz (in the entirety of it's context) -

Consider a capacitor with a voltage v(t) across it and current i(t) through it. Which of the following statement is most correct?

The time-varying voltage v(t) continuous.
The time-varying current i(t) continuous.
Neither i(t) nor v(t) are continuous.
Both i(t) and v(t) are continuous.
None of the above.

I said -
Neither i(t) nor v(t) are continuous.

Apparently the correct answer is -
The time-varying voltage v(t) continuous.


So how can a capacitor have continuous voltage while the current varies?
Am I missing something?

Thanks,

 

It's the varying that is continuous. As long as a current flows, the voltage on the capacitor is changing.

 

Q1) What does it mean for a waveform to "be continuous"?

Note that "varying" and "continuous" are two very different things.

Q2) What is the energy that is stored on a capacitor?

The energy must be continuous since if there were an abupt change in the energy stored on a capacitor it would mean that energy was either created or destroyed.

Q3) Can the energy in a capacitor be continuous if the voltage across it is not?

Q4) Can the energy in a capacitor be continuous if the current through it is not?

 

It's the varying that is continuous. As long as a current flows, the voltage on the capacitor is changing.

But that's not what the question is asking. It's asking whether there can be discontinuities in the voltage and or current waveform. Can the voltage be 10V one moment and 20V the next? Can the current be 10A one instant and 20A the next?

 

so you're saying that I read the question wrong?
it's not implying a constant voltage, but a constantly changing voltage?

 

No, it's not implying either.

What does it mean if you are told that a function is continuous?

 

so you're saying that I read the question wrong?
it's not implying a constant voltage, but a constantly changing voltage?

That's the way I see it. dv/dt is not equal to zero. but it took several readings to come to a conclusion. I think the question is poorly worded.

ps, It would also require several readings for me to understand what WBahn is talking about. Ima bit slow today.

 

No, it's not implying either.

What does it mean if you are told that a function is continuous?

continous as in the function exists in general?
but if that was the case then both would be continuous,

That's the way I see it. dv/dt is not equal to zero. but it took several readings to come to a conclusion. I think the question is poorly worded.

ps, It would also require several readings for me to understand what WBahn is talking about. Ima bit slow today.

thanks, that seems to make more sense

at least my knowledge of how capacitors function wasn't wrong, haha

 

Maybe I'm dense, but aren't you guys assuming this cap is in a DC circuit? I saw the question as a cap in an AC circuit, like an audio circuit. There the voltage and current is constantly changing with the wave form.

 

I don't think it's AC
We haven't even covered the idea that it might exist yet in the class
(also, got a 100 on the first exam...)

I'm pretty sure it's just a terribly worded question

 

I would have chosen None of the Above. The capacitor alone cannot force v(t) or i(t) to be continuous if a switch is thrown elsewhere in the circuit. Therefore v and i could be discontinuous, or not. There's not enough information to declare one or the other.

Obviously not what the instructor was looking for.

 

It is a perfectly valid and properly worded question. You just aren't clear on what is meant when a function is described as "continuous".

A continuous function is simply one that has no discontinuities -- meaning that it's value doesn't abruptly change at any point.

The two functions in the top of the graph are continuous but the function in the bottom is not.

Let's say that the three graphs supposedly represent the current in an inductor. The top two are possible but the bottom one is not. The reason is simple -- energy stored in an inductor is a function of current and any instantaneous change in current would mean an instantaneous change in the energy stored in the inductor, which can't happen without creating or destroying energy with infinite power. Hence, the current in an inductor MUST be a continuous function of time. This is why we have to put protection diodes in circuits that have inductors, because they will generate whatever voltage is required to keep that current flow continuous and if that means blowing out the transistor that is trying to shut the current off, then so be it. This is the whole basis behind how switch-mode power supplies and auto ignition circuits work.

The voltage across an inductor, on the other hand, has no such constraint. It can be discontinuous all day long.

So what is the analogous situation for a capacitor?

Answer that and you will understand why a capacitor (condenser) was placed across the points in an old-style auto ignition circuit.

 

yes, the answer was explained in class today, apparently by continuous he did indeed mean that the function was not broken, which is true for voltage of a capacitor, but not always (technically always, since all wires have inductance, but whatever) true for the current

 

I just thought it was a well disguised version of the old concept that one can't instantaneously change the voltage across an ideal capacitor. Unless you have an ideal voltage source connected across an uncharged ideal capacitor. Oops I probably shouldn't have suggested such a stupid thing.

 

I almost did earlier today but thought better of it.
Laying an ideal conductor across the poles of an ideal capacitor (no resistance) causes a discontinuity in the voltage. Unless you want to factor in the time it takes to move charges at the speed of light. I suppose "instant" is a relative term.

 

...
Let's say that the three graphs supposedly represent the current in an inductor. The top two are possible but the bottom one is not. The reason is simple -- energy stored in an inductor is a function of current and any instantaneous change in current would mean an instantaneous change in the energy stored in the inductor, which can't happen without creating or destroying energy with infinite power.
...

If energy changes abruptly => dE/dt = ∞ and thus power P= dE/dt = ∞.
Why is this impossible?

 

I almost did earlier today but thought better of it.
Laying an ideal conductor across the poles of an ideal capacitor (no resistance) causes a discontinuity in the voltage. Unless you want to factor in the time it takes to move charges at the speed of light. I suppose "instant" is a relative term.

Don't you just find that arc that occurs rather awesome.

 

If energy changes abruptly => dE/dt = ∞ and thus power P= dE/dt = ∞.
Why is this impossible?

Because energy can be neither created nor destroyed, but merely changed from one form into another. That is a process that happens at a rate -- the rate can be high, but it can't be infinite. It would be like having the volume of water in a tank of water change instantly from one gallon to two gallons. Can't happen because mass has to flow from outside the space to inside the space or be converted from something into water.

 

I just thought it was a well disguised version of the old concept that one can't instantaneously change the voltage across an ideal capacitor. Unless you have an ideal voltage source connected across an uncharged ideal capacitor. Oops I probably shouldn't have suggested such a stupid thing.

It wasn't disguised at all -- it flat out asked it.

 

It wasn't disguised at all -- it flat out asked it.

OK - somewhere between thinly disguised & blindingly obvious.