Capacitor charging/discharging for R=0

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In summary, In superconductors the current is always infinitely large but the voltage is not always infinitely large.
  • #1
amith_elec
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Consider an ideal capacitor its given to a switch and at t=t0 switch closes and Voltage =V is applied ..Consider R=0 in the circuit..how will the graph of i(current) v/s time(t) and Voltage (V) v/s time look like ?in all waveforms i have seen R is never zero..:confused:
 
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  • #2
amith_elec said:
Consider an ideal capacitor its given to a switch and at t=t0 switch closes and Voltage =V is applied ..Consider R=0 in the circuit..how will the graph of i(current) v/s time(t) and Voltage (V) v/s time look like ?in all waveforms i have seen R is never zero..:confused:

R cannot be zero.
In the theoretical case where it is, the current would be infinitely large for an infinitely short time.
I don't think the graph would tell you very much! (Even if it were possible to draw it)
 
  • #3
Stonebridge said:
R cannot be zero.
In the theoretical case where it is, the current would be infinitely large for an infinitely short time.
I don't think the graph would tell you very much! (Even if it were possible to draw it)

Why would the current be infinitely large? There are a fixed number of electrons in the capacitor and they must move some distance to discharge. Their speed is bound by the speed of light, so some time must elapse. So the current should be REALLY BIG, but not infinite.

Now saying I'm right, just wondering...

-David
 
  • #4
the graph of i vs t will be the delta function
(delta func;f(x); is zero at all values except at 0, where it is infinitely large such that the integral of f(x) from -infinity to +infinity is equal to some finite value[here, CV])
physically what happens in this ideal situation is that all the requisite charge is transferred to the capacitor plates in infinitesimal time. therefore, i~q/t;t tends to 0, so i tends to infinity.
 
  • #5
DavidSullivan said:
Why would the current be infinitely large? There are a fixed number of electrons in the capacitor and they must move some distance to discharge. Their speed is bound by the speed of light, so some time must elapse. So the current should be REALLY BIG, but not infinite.

Now saying I'm right, just wondering...

-David

That's what I said!
The resistance cannot be zero in practice. There would be a very large current for a very short time. The fact that we can talk about a current and a time means that there are numbers that can be assigned to them.
I stated that in the theoretical case when R=0 (which is impossible in practice in this situation) the current would be (theoretically) infinitely large. In the real world things don't go to infinity. In this case because the resistance can't go to zero.
Hope that makes it clearer.
 
  • #6
I think what the OP is asking is if the equation for current versus time (or time versus current) can be determined from the limit as R -> infinity.
 
  • #7
Stonebridge said:
That's what I said!
The resistance cannot be zero in practice. There would be a very large current for a very short time. The fact that we can talk about a current and a time means that there are numbers that can be assigned to them.
I stated that in the theoretical case when R=0 (which is impossible in practice in this situation) the current would be (theoretically) infinitely large. In the real world things don't go to infinity. In this case because the resistance can't go to zero.
Hope that makes it clearer.

i got the point ...also will the voltage across capacitor increase to supplied voltage instantaneously which i presume should happen if i is infinite (theoretically)...however,we study that voltage cannot increase instantaneously in a capacitor
 
  • #8
You are struggling with the difference between fields and circuits. There are no electrons in circuit theory just continuous current. A real capacitor has inductances that limit inrush current for example. Circuit answer is infinite current. Not physical answer.
 
  • #9
Superconductors have zero resistance they are used in MRI's
 

1. What is a capacitor?

A capacitor is an electronic component that stores electrical energy in the form of an electric field. It is made up of two conductive plates separated by an insulating material called a dielectric.

2. What is meant by "R=0" in capacitor charging/discharging?

R=0 refers to the resistance in the circuit being zero, meaning there is no resistance to the flow of current. In this case, the capacitor will charge and discharge rapidly.

3. How does a capacitor charge when R=0?

When R=0, the capacitor charges very quickly as there is no resistance to limit the flow of current. The electric field between the two plates of the capacitor builds up until the voltage across the capacitor is equal to the voltage of the power source.

4. What happens during discharging when R=0?

During discharging when R=0, the stored energy in the capacitor is released rapidly. The electric field between the two plates breaks down and the energy is released as a flow of current until the capacitor is fully discharged.

5. Is it possible for a capacitor to charge or discharge instantly with R=0?

No, it is not possible for a capacitor to charge or discharge instantly even with R=0. There is always a small amount of resistance in the circuit, and the charging and discharging process takes some time, albeit very short, to complete.

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