How Does a Capacitor React to a Sawtooth Wave Input?

[vig]

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...

 

[phyzguy]

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.

 

[vig]

'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?

 

[Redbelly98]

'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.

 

[vig]

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?...

 

[phyzguy]

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!"?

 

[Redbelly98]

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.

 

[vig]

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..