Battery connected to capacitor

[sophiecentaur]

Yeah I have to disagree with that one too

have hooked hundreds of capacitors across batteries no one of them has even got hot, let alone exploded

The only way it may explode is if the capacitor voltage rating is much lower than the applied voltage.
And many many years ago as a young learner I did explode a cap with a 150V rating when I accidentally placed 240V AC across it oops

Dave

I endorse your disagreement. The only way you will get 'too much' charge in a capacitor will be if there is some appreciable series Inductance in the circuit and that can lead to voltage magnification due to series resonance.
You are more likely to damage a Capacitor by Shorting it out, due to the potentially high discharge current. Any battery will have an appreciable internal resistance and limit the charge current.

 

[enorbet]

In actual practice capacitors connected to a DC source eg: a battery will not explode unless the dielectric breakdown voltage or the rated use temperature is exceeded. While in theory it is a capacitance problem, all real world capacitors have ESR which is Effective Series Resistance. In most cases this will bleed off any excesses in a system where battery and capacitor voltages match. They will reach an equilibrium, much like two batteries connected together.

 

[negation]

It is important to bear in mind that moving the plates together and apart involves WORK. As you take them further apart (not connected to anything) the charge is constant and the Capacitance decreases - so the PD increases pro-rata (Q=CV) and the Energy will increase (=CV²/2)If you move them apart when the battery is connected, the voltage is unchanged so the charge (Q=CV again) must flow back into the battery (more work done in shifting charge back against the battery emf).

In any of these problems, the way to get things straight is to apply the Formula, whenever you can and that will give you the right answer. You can rely on that answer, so it only remains to come to terms with it. If you try to approach it form the 'intuitive' direction (as a misplaced matter of principle) then you can fall over. Elementary stuff like this is totally reliable so it it never worth looking for an excuse for it being 'wrong'. i.e. you can rely on the book work. It is not a cop out.
When you have finally reached a stage in your Science Education that you are at the frontiers of Science and breaking new ground then you will need to start to doubt that what you have learned is 'enough'. Until then, stand on the shoulders of previous Giants (as Sir Isaac did). If you just don't want to learn the book work then that's up to you - very dangerous.

What about derivation? When does it become important? I often find it easier to see a map of the relationship between variables in the process of deriving certain equations. While it is VERY tedious, it does suits my mental stipulation. "just" applying formula isn't quite doing physics is it?

 

[sophiecentaur]

I couldn't agree with you more. Where does "derivation" come from, if not by using previous, established formulae (the formal statements of ideas)? Starting with the simple and going into the complex, step by rigorous step is the way things get found out - not arm waving and "no but what is really happening 'Physically'?"
The 'Giants' of the past, provide us with the building blocks of formal analysis of the way things work. The formulae have shown themselves to be the most reliable way of passing this stuff from brain to brain. How we, as individuals, deal with those formulae depends on our individual ability and application. Your "mental stipulation" shows that you have the 'right attitude' in my book.