How Does a Capacitor Discharge Over Time?

[Tobus]

Hi,

I am studying an engineering program in university. I have a piece of lab coursework to do and I am struggling to find information on it.
The lab report was based on 'The discharge of a capacitor with time using an oscilloscope'

It sounds silly but what is the theory of a capacitor discharging? I also need to find the principle of why is discharges relevant to the experiment at hand.

I know I'm asking a lot but I think I'm in the right place to ask :)

A huge thanks to anyone that can help me :)

 

[tiny-tim]

Hi Tobus!

From capacitor in the PF Library …

Inverse exponential rate of charging:

A capacitor does not charge or discharge instantly.

When a steady voltage $V_1$ is first applied, through a circuit of resistance $R$, to a capacitor across which there is already a voltage $V_0$, both the charging current $I$ in the circuit and the voltage difference $V_1\,-\,V$ change exponentially, with a parameter $-1/CR$:

$$I(t) = \frac{V_1\,-\,V_0}{R}\,e^{-\frac{1}{CR}\,t}$$

$$V_1\ -\ V(t) = (V_1\,-\,V_0)\,e^{-\frac{1}{CR}\,t}$$

So the current becomes effectively zero, and the voltage across the capacitor becomes effectively $V_1$, after a time proportional to $CR$.

 

[Tobus]

Hey thanks :)

Thank you for the help,

For my introduction I have written this,

"We are doing this experiment to understand if the capacitor discharges at a particular rate to show that the theory of a capacitor discharges at an exponential rate when a direct current is removed. Capacitors are used in many circuits and electronic storage devices. As the capacitor is charged from the direct current supplied there is a force of attraction between the two plates as one becomes positively charged and the other becomes negatively charged. Once the charge/voltage? has been removed the capacitor starts to discharge and the flow of electrons moves across the plates. The rate of discharge decays exponentially to time."

What do you think, do I get my point across properly? More importantly is the physics correct! lol

 

[tiny-tim]

As the capacitor is charged from the direct current supplied there is a force of attraction between the two plates as one becomes positively charged and the other becomes negatively charged. Once the charge/voltage? has been removed the capacitor starts to discharge and the flow of electrons moves across the plates. The rate of discharge decays exponentially to time.

Hi Tobus!

hmm …

i] the electrons do not move across the plates … they go the long way round!

ii] you haven't actually explained anything … why do the electrons go the long way round (especially when, as you point out, there's an attractive force the short way round) … and why is it exponential, or at least, what is the governing equation?

 

[Tobus]

What do you mean by long way around :S. Sorry I'm not so sure lol.
I know its exponential decay as the current decreases at the same ratio in successive equal intervals of time.

How about that? Do you think I should put it in somewhere.

For my introduction I simply need to explain the theory of what a capacitor does. :)

 

[tiny-tim]

What do you mean by long way around :S.

Again from PF Library:

Displacement current:

No current ever flows through a functioning capacitor.

But while a capacitor is charging or discharging (that is, neither at zero nor maximum charge), current is flowing round the circuit joining the plates externally …​

I know its exponential decay as the current decreases at the same ratio in successive equal intervals of time.

but why? (how does it know? )