Why Does the Voltage Across a Capacitor Lag Behind the Input Voltage?

[p75213]

Homework Statement

Can somebody explain why the voltage across the capacitor (v0) lags vi?

Homework Equations

The Attempt at a Solution

 

[p75213]

I proved it with a vector diagram.
Let I be the reference phase ie. 0 degrees. Because the voltage across R is in phase with I it also has 0 phase.
The capacitor voltage V0 lags I by 90 degrees ie. -90
Vi=V0+Rvoltage.
This shows Vi vector after I (R voltage) but before V0.
Therefore Vi leads V0.

I still would appreciate a more intuitive explanation if somebody has one.

 

[rude man]

My old ARRL handbook explained this in a non-calculus way. I never bothered to try to understand it. It was obvious to me once I had diff eq's and transform techniques - meanwhile, I believe yours is the best intuitive explanation there is.