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In my introductory electrical class there was a question with a scenario that completely confused me.

It asked what the current drawn by a 1000uF capacitor would be after 10ms if it was connected to a 120V source.

Wouldn’t a capacitor connected to a voltage source with no resistance charge instantly and draw an infinite amount of current in this scenario?

The rest of the problem was dependent on this calculation like it’s supposed to be a finite number.

We haven’t even discussed RC circuits in this class and have only done problems similar to this with a current source instead where you could calculate voltage by the integral form of I=C*dV/dt.

How were you supposed to answer this problem?

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    \$\begingroup\$ Is the source AC or DC? \$\endgroup\$
    – Hearth
    Oct 25, 2023 at 14:34
  • \$\begingroup\$ It's DC we haven't talked about AC circuits at all. \$\endgroup\$
    – lizaerd
    Oct 25, 2023 at 14:38
  • \$\begingroup\$ The problem would make some amount of sense if it was an AC source, but for a DC source it doesn't. Are you sure there's no extra information given about the source or capacitor, like an ESR or anything? \$\endgroup\$
    – Hearth
    Oct 25, 2023 at 14:48
  • \$\begingroup\$ No the only info given was the capacitance of the capacitor, the voltage of the source, and the time. \$\endgroup\$
    – lizaerd
    Oct 25, 2023 at 14:58

2 Answers 2

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Wouldn’t a capacitor connected to a voltage source with no resistance charge instantly and draw an infinite amount of current in this scenario?

Yes, unless it already contained the correct charge when connecting. Either way, after 10ms there would be no current.

Now a real-world 1000µF capacitor with a voltage rating of >120V will be an electrolytic capacitor with significant inductivity and resistance. 10ms is a comparatively long time (after all, such capacitors are often used as auxiliary phase motor starters at frequencies of 60Hz).

If we take a look at the required charge, it will be 120mC which costs the voltage source 14.4J of energy. Getting it there in 10ms requires a power of 1.44kW. The capacitor will contain only half that energy, the rest is turned into heat in parasitic resistance.

So while the question is easy to answer in theory, once you turn to real-world circuitry, things become quite more squishy.

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    \$\begingroup\$ It's not necessarily an electrolytic capacitor. I've used a 1500 μF 1100 V film capacitor before. It was about the size of a 2-liter soda bottle, and cost over $100, but they do exist. \$\endgroup\$
    – Hearth
    Oct 25, 2023 at 15:01
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a 120V source

120V smells like a 60Hz AC source. For that, the capacitor current is finite and leads the voltage, and you get it from Ohm's law applied to capacitive reactance at 60Hz. That may well be what was meant.

If it's 120V DC then there's an infinitely high current spike lasting an infinitesimal time, followed by no current flow.

The rest of the problem was dependent on this calculation like it’s supposed to be a finite number.

Zero is a finite number, and it is a reasonable approximation in practice for 120VDC across a 1000uF capacitor, tested 10ms after application to a discharged capacitor.

there was a question with a scenario that completely confused me

I presume you asked here because you asked the teacher first and they didn't answer? :) If the teacher doesn't answer, you can complain to their superior if you wish, since that would be a wee bit on the side of majorly failing basic job requirements for a teaching position. Read this in the tone of "a very minor case of serious brain damage, but don't be alarmed", as the wise Wheatley uttered.

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