>> Take a capacitor: initially it's discharged. Now connect it to a voltage 
>> source, the first instant you do, the voltage across the capacitor is 
>> still zero
>
> How on earth do you work that one out?
>
> If you connect a capacitor to a 9 V source, then the potential difference 
> across the capacitor is... exactly 9 V. In which universe is that 0 V?

A 9V source has an internal resistance, which will initially take all the 
voltage as the capacitor draws a huge amount of current (even if it doesn't, 
the wires will have some resistance).  So across the capacitor terminals 
will be a very low voltage, but a very high current through it.  Once the 
capacitor is fully charged, there will be no current flowing, and so no 
voltage drop across the internal resistance, and then the full 9 V across 
the capacitor.

So you see, in this simple case, voltage across the capacitor is definitely 
not proportional to current flowing through it.  Quite the opposite to a 
resistor.

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