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When you turn on a switch between a battery and capacitor, there is an inrush of current, but we measure zero volts across the cap because it is effectively shorted at this instant. As the cap charges, current drops and voltage rises. When it's fully charged, the voltage is max, and no more current flows.

If we put AC across the cap, it does this every half cycle. Max, current, zero volts, building up to max voltage, zero current. Then it does this for the other half cycle.

If we plot this on a graph, the voltage goes from zero to max at the same time current goes from max to zero. We say that "The voltage lags the current". Do this over several cycles and you'll have a sine wave for voltage and cosine wave for current. Sine and cosine are 90 degrees out of phase.

Here's more information: http://www.allaboutcircuits.com/vol_2/chpt_4/2.html

Q: How capacitor introduces phase difference of 90 between voltage and current?

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