What Is the Role of Displacement Current in an RC Circuit?

[ecy5maa]

In an RC circuit shown below, with the switch closed after a long time, when the capacitor is charging, there is a current across the capacitor given by Initial current x e ^ (-t/RC)...

Is this current...the current supplied by capacitor to the rest of circuit, or simply the current across the capacitor?

http://apricot.polyu.edu.hk/~lam/cp/img/rc-circuit.gif"

 

[tiny-tim]

hi ecy5maa! happy new year!

(try using the X² icon just above the Reply box )

no current flows across a capacitor … it's a complete insulator (unless, of course, the applied voltage is so extremely high that a spark can jump) …

the electrons have to go the long way round! ​

 

[ecy5maa]

Happy new year too you too :)


What did u mean by currents have to go the long way around?

Anyway eventually i agree that there will be no current across a capacitor. But what about while its charging? there will be voltage across it, and shouldn't that mean a current also flows?

 

[tiny-tim]

But what about while its charging? there will be voltage across it, and shouldn't that mean a current also flows?

current can't flow across it, there's a gap!

voltage is just electric potential difference, it doesn't mean there's a current (there's no current between the poles of a battery if there's no external connection, but there's still a potential difference! )

 

[ecy5maa]

http://apricot.polyu.edu.hk/~lam/cp/img/rc-circuit.gif"
Uhh...so what you are saying is the current goes from the +Vc towards +Vb in anti clockwise direction?But it won't go from +Vc to -Vc to -Vb to +Vb and so on in a clockwise direction?

 

[tiny-tim]

that's correct …

it can't go across the gap

(btw, that's why the symbol for a capacitor has a gap in it! ) …

it has to go the long way round, through everything else

 

[ecy5maa]

Thank you for all the help :)

Ok I was actually working on this question (attached below)

We have to find the current through the resistor R11 after the switch is opened. ( it was shut for a long time prior to it opening at t=0)

Everything is correct but my final answer is wrong.

Shouldnt The current due to the 8v source also flow through R11 in the same direction as the current due to the capacitor... flowing through R11.

The final answer, is Current due to 8V source minus the current due to the capacitor.



I don't get that!



P.S I can clarify further if needed

 

[yungman]

In an RC circuit shown below, with the switch closed after a long time, when the capacitor is charging, there is a current across the capacitor given by Initial current x e ^ (-t/RC)...

Is this current...the current supplied by capacitor to the rest of circuit, or simply the current across the capacitor?

http://apricot.polyu.edu.hk/~lam/cp/img/rc-circuit.gif"

What do you mean by this? Do you mean

1) Initially the switch was open and the cap discharged, then you close the switch.

OR

2) Do you mean you closed the switch and wait for a long time so the voltage on the cap is in equiblium?

For 1) the moment the switch close, there will be current flow. Current is displacement current instead of conduction current. As the cap charge up, current decrease and eventually become zero and cap do not have conduction current since it is not physically connected together.

For 2) No current at all since the cap consist of two insulated plate and no conduction current can pass through. Current only flow as displacement current when the cap is charging up.

 

[ecy5maa]

Current only flow as displacement current when the cap is charging up.

yes...this is what i was asking. What exactly do we mean by displacement current and in Which direction would the displacement current flow?

 

[yungman]

yes...this is what i was asking. What exactly do we mean by displacement current and in Which direction would the displacement current flow?

Displacement is in the same direction from the +ve of the battery through the resistor through the cap back to the -ve side of battery. When the cap is charging, there is not difference from a conducting circuit. You just have to keep in mind the electrons are not physically passsing across the capacitor. Instead you think of the electrons are accumulate on the side of the cap that connected to the -ve side of battery and the electrons are leaving from the top side of the cap, through the resistor and to the +ve side of the battery. ( Current is opposite direction of electrons flow ). Since no electrons just the cap, accumulating charges will result in building up of potential across the cap and in your case, eventually the cap will be charged up to the voltage of the battery and the current flow stop.

I think "displacement current" is the term used specially for the capacitor that in AC condition, it behave as if the current flowing through the cap, but in fact nothing really pass through. Instead AC current only result in charging and discharging of the capacitor. That is the reason why capacitor only pass AC current but not DC current. I am not very good in definition, this is my understanding. The term usually link to this equation in EM books:

$$\int_S \nabla X \vec H \cdot d \vec S \;=\; \int_S \vec J \cdot d \vec S \;+\; \int_S\frac{\partial \vec D}{\partial t}\cdot d \vec S = I_c \;+\; I_D$$

Where first term is conduction current and the second is the displacement current. The $\vec D$ is the electric field density in the cap in your case. Check out the EM books, they use the exact circuit like what you have to explain conduction and displacement current density.

So in your case, during charging, current pass through resistor as conduction current. BUT the same amount of current pass through the cap as displacement current, after leaving the cap, the current become conduction current and back to the -ve side of the battery.