Voltage in Capacitor vs. Power Supply: Conceptual Question Answered

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SUMMARY

The voltage across a capacitor can equal the voltage of the power supply under specific conditions, particularly in circuits with inductance. Inductance can create a phenomenon known as "ringing," where the voltage overshoots the intended value due to current momentum, observable on an oscilloscope. Additionally, even in the absence of inductance, the voltage can match the supply voltage within the limits of one elementary charge due to the discrete nature of charge carriers and thermal energy effects.

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Homework Statement




I am just wondering, can the voltage in a capacitor ever be equal to or greater than the voltage in the power supply? Probably not the power supply...but is it possible to be equal to?




The Attempt at a Solution

 
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In a real circuit where there's always a bit of inductance at play, sure. Inductance causes what might be taken as a sort of current momentum that can cause an "overshoot" of the charging "goal" potential difference. When there's more than just a whisper of inductance at play, you can get what's called a "ringing" after abrupt changes in driving voltage -- a decaying oscillation around the final value. This can be seen easily on an oscilloscope view of the voltage in a circuit, such as where a square wave is driving a circuit.

Even if there were no inductance, the capacitor voltage can end up equal to the supply voltage +/- the effect of one unit elementary charge, since the charge carriers come in discrete size. Momentum coupled with random processes due to thermal energy will also slosh the charges around the equilibrium point to some extent.
 

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