Why cant voltage across a capacitor change instantaneously?
To change the charge in a capacitor, you must either add or remove electrons from the plates. these electrons have a mass and they have a limited speed at which they can travel. therefore, it takes time for the charge to change, no matter how large the force is trying to move it.
The voltage across a capacitor is proportional to the capacitor plate load. Therefore, to change the voltage, you must add or remove a load. to change the charge instantly, you will need an infinite current. this is simply not possible because an infinite current is not possible, not to mention the weak but inevitable parasitic inductance and resistance in capacitor conductors and plates that will also slow it down. very fast is possible, instant is not. because in this case, the current flowing from / to the capacitor would be infinite.
this is not possible for two reasons:
the capacitor must be ideal and the circuit connected to the capacitor (in fact, it must be a short circuit) ideal 0 – superconducting impedance.
Even if the first case is filled, the electrons in the capacitor have a mass, a limited number of them, they can not accelerate instantly and there is not an infinite amount, the current can not not be infinite.
think of a container filled with water with a discharge port. you can not draw as much water at a time as the hole allows. or think of a carriage on a steep road. you push it, and it takes time to push it to the limit.
Similarly, a capacitor can only discharge at a given current rate; it takes a while before he discharges himself. the voltage being proportional to the charge will change slowly, to the rhythm of the passing current.
can we say that because of the existing resistance (which may be an internal resistance in the source or an external resistance in the circuit) in the path between the source and the capacitor, the capacitor is unable to charge (to from the source) instantaneously, that is to say in a zero time .then the voltage source needs infinite power to move the entire load on the capacitor in zero time.
In technical terms, is because the voltage across a capacitor is proportional to the time integral of the load that feeds it. The electric charge transfer rate is equivalent to the electric current, which causes an instantaneous change in the voltage across a capacitor. you would need either (a) an infinitely small capacitor, or (b) power it with an infinitely large current.
It is intuitively obvious that to instantly change the water level of the tank, you need either (a) a tank of infinitesimal volume, and / or (b) a system to feed the tank with water at a speed infinitely high. the water pressure is similar to the electrical voltage and the water flow is similar to the electric current.