How Does a Capacitor React to a Sawtooth Wave Input?

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Discussion Overview

The discussion centers on how a capacitor reacts to a sawtooth wave input from a function generator, exploring the waveform produced across the capacitor in both ideal and practical scenarios. Participants examine the implications of circuit elements such as resistance and inductance on the behavior of the capacitor.

Discussion Character

  • Exploratory
  • Technical explanation
  • Debate/contested

Main Points Raised

  • One participant questions whether the voltage across the capacitor would match the sawtooth waveform or be smooth due to the capacitor's inability to change voltage abruptly.
  • Another participant suggests that in an ideal scenario with an ideal voltage generator and capacitor, the waveform could show sharp peaks, but acknowledges the impracticality of such conditions.
  • It is noted that the current into a capacitor is proportional to the rate of change of voltage, implying that an instantaneous change would require infinite current, which is not feasible in real circuits.
  • Participants discuss the impact of adding a resistor in series, with one asserting that it would limit the current and alter the waveform, while another emphasizes that the inability to achieve sharp voltage changes is due to the source's limitations.
  • A metaphor involving filling a swimming pool is used to illustrate the concept of limitations in current supply, prompting further debate on the analogy's validity.
  • Some participants highlight that real capacitors and connecting wires have resistance and inductance, which contribute to the limitations on current and voltage changes.

Areas of Agreement / Disagreement

Participants express differing views on the implications of ideal versus real-world scenarios, with no consensus reached on the nature of the waveform across the capacitor or the validity of the analogies used.

Contextual Notes

Limitations include the assumptions of ideal components versus real-world behavior, the dependence on circuit configurations, and the unresolved nature of how various factors interact in practical applications.

vig
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Capacitor---very basic questions

Ive already gone through many posts on working of capacitors...but if i consider a very simple circuit...say i connect a function generator (which generates a sawtooth wave) across a capacitor...(no resistance in series)...and i measure voltage across the capacitor, what will be the waveform like?..one theory says that since the capacitor is connected in parallel to the function generator, i must get the same sawtooth waveform..however, voltage across capacitor can not change abruptly and so i should be getting a smooth waveform across it..it would be great if someone can clear things out...:smile:
 
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If it is an ideal voltage generator, and an ideal capacitor, the voltage generator will supply the infinite current necessary to get an abrupt change in the voltage across the capacitor. In practice, both the capacitor and the voltage generator have some resistance and some inductance, and the voltage generator is limited in the amount of current it can supply. These non-ideal elements will determine exactly what the waveform looks like.
 


'voltage generator will supply the infinite current necessary to get an abrupt change in the voltage across the capacitor'...could u pls elaborate on this?..and considering the most ideal situation, the waveform across a capacitor would show sharp peaks??...and if a resistor is connected in series, and the function generator can still source infinite current (say), the waveform would remain the same?
 


vig said:
'voltage generator will supply the infinite current necessary to get an abrupt change in the voltage across the capacitor'...could u pls elaborate on this?..
The current into a capacitor is proportional to the rate of change of the voltage across the capacitor. An instantaneously abrupt change in voltage represents an infinitely large rate of change for the voltage, therefore the current would have to be infinite to produce such a voltage change across a capacitor.
and considering the most ideal situation, the waveform across a capacitor would show sharp peaks??...
Yes, in this idealized and very impossible scenario physguy described, that is exactly what would happen. (Ignoring that pesky detail about it being impossible.)
and if a resistor is connected in series, and the function generator can still source infinite current (say), the waveform would remain the same?
No, a resistor limits the current that an ideal voltage source would produce.
 


Redbelly98 said:
The current into a capacitor is proportional to the rate of change of the voltage across the capacitor. An instantaneously abrupt change in voltage represents an infinitely large rate of change for the voltage, therefore the current would have to be infinite to produce such a voltage change across a capacitor.

Yes, in this idealized and very impossible scenario physguy described, that is exactly what would happen. (Ignoring that pesky detail about it being impossible.)

No, a resistor limits the current that an ideal voltage source would produce.

so very crudely speaking...its not a capacitor's fault that it does not allow a sharp change in voltage..it is essentially the inability of the source to provide an infinite current?...
 


vig said:
so very crudely speaking...its not a capacitor's fault that it does not allow a sharp change in voltage..it is essentially the inability of the source to provide an infinite current?...

Suppose I'm trying to fill a swimming pool. Would you say, "It's not the swimming pool's fault that it doesn't fill up immediately, it's my inability to find a big enough hose!"?
 


vig said:
so very crudely speaking...its not a capacitor's fault that it does not allow a sharp change in voltage..it is essentially the inability of the source to provide an infinite current?...
Not quite. A real capacitor has some resistance, as do the connecting wires. And any closed circuit has a nonzero inductance too. So there are several factors at play that limit the current.

If we spent more time thinking about how real devices behave, we might come up with other factors too.
 


phyzguy said:
Suppose I'm trying to fill a swimming pool. Would you say, "It's not the swimming pool's fault that it doesn't fill up immediately, it's my inability to find a big enough hose!"?
Is'nt it true?..if u could get a big hose then the swimming pool would fill up immediately..:rolleyes:
 

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