Charge a Capacitor: Qualitative & Quantitative Explanations

[person_random_normal]

I understand the situation when we charge a capacitor using a battery and a resistor placed in between serially placed ! V = iR + Q/C where we write i = dQ/dt
whereas,
V is voltage of battery
R is resistance of resistor
Q is charge on capacitor
C is capacitance of capacitor
i is current
But what happens when we connect a capacitor directly to a battery , nothing in between ??
Can somebody explain this qualitatively and also quantitatively !

 

[Dale]

There is always some resistance in the wire. So just take the RC circuit you already know and make R very small.

 

[person_random_normal]

But what if the wire connecting the battery and the capacitor is of zero resistance
That my question actually ! !

 

[nasu]

The capacitor will charge instantaneously. An "infinite" current will flow for no time (zero time interval) so that it caries a charge Q=E/C where E is the emf of the battery.
But this does not describe what happens when you connect a (real) battery to a (real) capacitor.

 

[Dale]

But what if the wire connecting the battery and the capacitor is of zero resistance
That my question actually ! !

Just take the RC circuit that you already understand, calculate whatever quantity you are interested in, and then take the limit as R goes to 0. It will give you mathematically what nasu described above.

 

[person_random_normal]

Actually i want to ask how do we apply krichhoff' s law for a circuit having only a battery(ideal, of zero resistance) and a capacitor
I got to know something like -energy radiated out in form of EM waves, as of a reference in my textbook
but that is not in detail , so can somebody please elaborate on that

 

[nasu]

E=Q/C

 

[Dale]

Actually i want to ask how do we apply krichhoff' s law for a circuit having only a battery(ideal, of zero resistance) and a capacitor
I got to know something like -energy radiated out in form of EM waves, as of a reference in my textbook
but that is not in detail , so can somebody please elaborate on that

What do you get if you use the approach I already suggested above?

 

[stedwards]

See 4 other Charging of capacitor threads.

 

[CWatters]

Actually i want to ask how do we apply krichhoff' s law for a circuit having only a battery(ideal, of zero resistance) and a capacitor.

That's a bit like asking what happens if you apply an infinitely large force to an immovable object. In the real world the capacitor will also have some resistance and inductance.

If you connect an ideal battery to an ideal capacitor using ideal wire the current would be infinite. However the capacitor would also charge up in zero time so the infinitely large current would only flow for an infinitely short time.

I got to know something like -energy radiated out in form of EM waves, as of a reference in my textbook
but that is not in detail , so can somebody please elaborate on that

How best to explain? .. The voltage on the wire/capacitor would rise very fast in the situation you describe. That's equivalent to having a very high frequency signal on the wire. In general the higher the frequency the shorter the aerial you need to easily launch a radio wave. So yes you would get a burst of radio waves. An AM radio receiver would probably pick it up as a click or thump.

Other interesting things might happen. For example if you pass a high current through a wire in a magnetic field it will experience a force. After all that's how a motor works. You propose passing an infinite current through a wire in the Earth's magnetic field.