After searching Internet and also text books, I wonder why there are not many conclusive discussions about this question "What if the resistor value in an RC Circuit is equal zero?". Anybody could give a good explanation please? Thanks!

 

According to the math.......with zero resistance......the charge time should be zero........meaning instantaneously charged.

But even with a resistance free cap.......it would take a certain amount of time. At the present time....we don't have resistance free circuits. So probably not too much info on it.

Resistance free circuits will be quicker.......more efficient.....but not instantaneous. And will require new equations.

Electrical pressure....at best, travels at c. That takes time. ANY length....takes time. Which means all events have duration.

Even Scotty on the Enterprise NCC-1701......going at warp 10.......needs time to move one foot.

 

Capacitor has its own resistance, ESR, equivalent series resistance. This means that resistance is ALWAYS present, it is the integral part of the device.
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Hello,

Only an ideal capacitor will have no resistance.
A real capacitor will have ESR, leakage resistance and inductance:



See this page for more info:
https://www.powerguru.org/electrolytic-capacitor-lifetime-estimation/

Bertus

 

It should be a fairly obvious exercise to imagine what happens in the limit as the R in an RC circuit is reduced to zero. RC approaches zero as R approaches zero. As the time constant approaches zero a capacitor with no resistance will charge and discharge very quickly. You can see this quite clearly in the series expansion for the exponential function. The leading term is 1 and the rest of the terms disappear. You can also see this in the graph of the exponential function.

 

After searching Internet and also text books, I wonder why there are not many conclusive discussions about this question "What if the resistor value in an RC Circuit is equal zero?". Anybody could give a good explanation please? Thanks!

Hello there,

This is a good question but to answer it we have to know what level of physical reality you choose to allow.

That's because taken at face value we end up with a result that is not allowed anywhere in our universe, which would have to allow an infinite current which is not deemed possible even though there may be no voltage drop. If however you choose to allow an infinite current because in theory we can say there is such a thing, then the result would be that the cap charges instantly to a value determined by the duration of the current pulse, and because if the current pulse was longer than what we call "delta t" where delta t approaches zero then it would require an infinite amount of energy and it would charge to an infinite voltage level. So you start to see how meaningless this scenario turns out to be. At the present point in time we dont believe there is anything like an infinite source of energy. If we can stick to pure theory though then we can say that we can have an infinite current for an infinitesimally short time period, and that can cause the cap to shoot up to a finite voltage level. That would be known as the impulse response of the cap. That's not possible in the real world however except as an approximation.

A more practical result would come from assuming some finite distances for the circuit, such as the physical size of the cap and the connection lengths. Even if we assume R=0 and any parallel R is infinite (G=0) we still have the physical lengths to deal with, so we end up with what is known as a lossless transmission line. We would then be dealing with a real physical scenario where the step change in voltage at the input side would take some finite time to set up a current in the capacitor due to the speed of light limitation, and that would govern the whole process. The general solution to this somewhat still ideal but more realistic situation is known as the Telegrapher's Equation, which is an equation for transmission lines. That also has an underlying assumption too though, that there is no radiation. Radiation would show up as an energy loss so not all energy would be transferred from the exciting source to the capacitor.

We are assuming a step change i believe, but if we move to a purely AC circuit we end up with a very practical circuit where the source transfers energy to the cap and the cap transfers energy back to the source in turn, depending on the point in time we look at it. This is actually a common circuit used worldwide.

 

Thank you all for your answers which give me a new perspective to analyze the RC circuit.