Infinite current required to change capacitor voltage instantaneously?

[CoolDude420]

Homework Statement

We just started capacitors in class and we were introduced to the formulae q=CV and i = C*dV/dt
In the notes it said that if the voltage across a capacitor were to change instantenously, the capacitor current would be infinite.

It goes on to say why this is never possible. But what I don't understand is, how would the capacitor current be infinite if the voltage did change instantaneously? How did he come to that conclusion that the current would be infinite due to a voltage change.

Homework Equations

The Attempt at a Solution

 

[Mark44]

Homework Statement

We just started capacitors in class and we were introduced to the formulae q=CV and i = C*dV/dt
In the notes it said that if the voltage across a capacitor were to change instantenously, the capacitor current would be infinite.

It goes on to say why this is never possible. But what I don't understand is, how would the capacitor current be infinite if the voltage did change instantaneously? How did he come to that conclusion that the current would be infinite due to a voltage change.

It's a result of the dV/dt factor, the instantaneous rate of change of voltage.
Suppose the voltage at time t = 0 is 0 V. and the voltage sometime later.
If the voltage increases to 12 V in 1 second, what's $\frac{\Delta V}{\Delta t}$? (I.e., what's the average time rate of change of voltage?)
What if the increase happens in .1 second? In .01 second? In .001 second? And that's still not instantaneous. With ever shorter time intervals, what happens to $\frac{\Delta V}{\Delta t}$?
Current i is directly proportional to dV/dt, so as dV/dt gets larger, so does i.

 

[David Lewis]

Instantaneous voltage change means zero capacitive reactance, so you'd have 3 sources of impedance left: loss resistance, inductive reactance, and radiation resistance.