#Derivation of magic battery series#

If the capacitor value (Farads) is gigantic, a great big current will be drawn, and the internal resistance of the battery will drop nearly all of the voltage generated by the battery, causing the voltage differential between the battery terminals to drop to a very very small value. That alone is sufficient to cause a rise-time in the charge of the capacitor. The internal resistance of the battery also prevents infinite current. The resistance of the wires, small though it may be, prevents infinite current. In the lab, even if you connect a battery to a capacitor, reality keeps you from destroying the universe. There is _nothing wrong with this_, because we've already discounted that any heat/work is created by ignoring lead resistance, and by the same simplification, we've ignored the capacity of the plates (which would fill instantly without resistance.) Which is also OK, because then we can add an in-line resistance in the form of a perfect, ideal resistance, whose value is exactly what we say it is in ohms, and which doesn't have _any_ capacitive or inductive characteristic. If we are working in a simplified 'ideal' system, we presume that the voltage which is marked on the battery is delivered to the terminals of the capacitor, which immediately begins to draw infinite current. In order to understand how the math models the action of the active and passive components, it really helps to understand the real basic tenets of electricity and electronics:ДЎ) There are no ideal components: Wires have resistance, batteries and capacitors have leakage currents, inductors' effects are weakened by eddy currents (induced into any nearby metal including their own windings) and even at initial conditions (i.e., immediately upon connection of voltage across an inductor) have resistance which limits currents from becoming infinite.Дў) Only when you simplify equations to make calculations easier, do you run into impossible situations, which are dissolved by adding back the things removed to make things simpler.ДЄn example: A battery connected to a capacitor. Unfortunately, much of the literature is confusing but it is much better now than in my early learning days.Д¬lick to expand.Of course, this is not at all true in the Real World: Only in the theoretical world can we lay claim to perfect batteries, capacitors, inductors, wires, etc. You need to understand electronics and understand mathematics to relate the two effectively. Thus di/dt= 1ДЄs you imply with your question, applying mathematics to electronics is quite difficult and is one of the great failings in electronics in general. Thus, if you apply 1V across an inductor of 1 Henry the current will increase at a rate of 1 Amp per second. (2) If you force a current through an inductor an infinite voltage will be generated.Д«ut, in practice, if you apply a constant voltage to an inductor the current through the inductor will increase linearly for ever. Thus, if you force a constant current of one Amp into a capacitance of 1 Farad, the voltage across the capacitor will increase by 1V per second. (1) If you apply a voltage to a capacitor an infinite current will flow.Д«ut, in practice, if you force a constant current into a capacitor the voltage across the capacitor will increase linearly for ever. A third, and more basic tenant, is that you cannot place a short circuit across a voltage source, because an infinite current will flow. The other is that you cannot force a current through an inductor because an infinite voltage will be generated. You can also connect a perfect constant current source to a capacitor or inductor as long as there is a resistor in parallel with the constant current source.Д¬lick to expand.I was being flippant vead because it is one of two related impossibilities in electronics.

#Derivation of magic battery series#

All REAL situations will have a component of resistance in the circuit so you can connect a perfect battery to a capacitor or inductor in series via a resistor. If you connected a perfect constant current source to an inductor the inital voltage would be infinity. Also you can connect an inductor to a constant voltage source (A perfect battery.) but again you must specify a time as the current will evenually reach infinity. Asking the question with an example of a capacitor connected to a constant current source would be valid provided you also specified a reasonable time that it was connected as the voltage would eventually reach infinity. The way you asked the question shows that you do not understand the way capacitors and inductors behave.

This is **broken link removed** which should answer your question. If you Google ' derivation of capacitor charging equation' you will get many hits.