The answer is related to the fact that the maximum part of the sine wave in the wall socket is really 170 volts, instead of 120. In other words, the true "peak voltage" is 120 times the square root of 2, which is about 170 volts.
Then why is it called "120 volts?" Because a sine wave with a 170 V maximum ("peak") has an "effective" value of 170 divided by the square root of 2, or 120 V, so we call it "120 volts." (The square root of 2 is 1.414, and 1/(1.414) is 0.707, which are numbers that are used a lot in electronics.)
It turns out that to determine the effective value of a sine wave, you have to do the following. First divide up the top half of the ac into very small slices (the "increments" of calculus), and then square each one of these short-term voltages.
The next step is to figure out the average value (the "mean") of these squared slices. Then take the square root of this mean. This is called the "root mean square" voltage, or "RMS."
It is not the same as the simple average, and also it does not work for odd shapes such as sawtooth waves. This 120 volts RMS of ac, pushing sine wave current through a certain resistance, produces the same amount of heat power that a steady dc 120 volts would produce, going through that same resistance.
The peak voltage would give a falsely high estimate, because it only exists for very short times, so it is not used for these purposes. We therefore call the wall socket electricity "120V" (or "240V" in many European countries), even though the peak is higher.
However, the capacitor eventually charges up to the full peak voltage.
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