# Voltage across a capacitor can't change abruptly because

1. Sep 9, 2008

### Andrew123

current would need to be infinite for this. Why is this. Can anyone show the maths behind this? Cheers!

*EDIT* ok i just did some maths on a basic RC circuit. If t approaches zero then the current simply approaches -(Vi/R).. which isnt infinite. This is why i can't grasp this. I would love to see the theory behind why this is. TY

Last edited: Sep 9, 2008
2. Sep 9, 2008

### MATLABdude

$$i_{c}(t)=C\frac{dv_{c}(t)}{dt}$$

The rest is left as an exercise to the reader ;-)

HINT: a limit is involved.

Voltage can change instantaneously in a capacitor... But only if single charges are being applied to the plates (Single Electron Transport devices)--this is near the cutting edge of research.

3. Sep 9, 2008

### Andrew123

Yeah limit t ---> 0 and I -----> infinity yah? however dv/dt = lim change in t --> 0 [change in V / change in t] so if we are already limiting change in t towards zero then how can we do this doubly so?

4. Sep 9, 2008

### MATLABdude

I don't understand what you mean by:
dv/dt = lim change in t --> 0

Take the limit as dv/dt goes to infinity (instantaneous voltage change).

5. Sep 9, 2008

### Andrew123

but what sends dv/dt to infinity?

6. Sep 9, 2008

### MATLABdude

That's the definition of an instantaneous voltage change (finite change in voltage in 0 time). You might have rising or falling voltage (say, 0 to 5 V or 5 V to 0V), but really, the idea is the same (infinite current).

7. Sep 9, 2008

### Andrew123

Sorry but still why does the current need to be infinite?

8. Sep 9, 2008

### Defennder

If you want the the voltage to change instantaneously, that means you want dV/dt to be as large as possible, approaching infinity, right? Remember that changing instantaneously means that on the V/t graph you want to have a vertical line at one point and not a smooth continuous one. Now, what is the gradient of a line which is very nearly vertical? What happens if it is vertical? Now what does dV/dt equal to?

9. Sep 9, 2008

### MATLABdude

If $$\frac{dv}{dt}$$ goes to infinity so must C (a constant) times this number. Since this quantity happens to be the current...

10. Sep 15, 2008

### cabraham

A capacitor with charge has energy. W = C*(V^2)/2. A change in voltage requires a change in energy which requires that work be done. If voltage changes instantly, then dw/dt = power is infinite. A source of infinite power does not exist (well, actually it does, but we are discussing science in the real world, and not theology).

Infinite power would result in infinite current for an instant as p = v*i.