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I have a basic quesiton about circuit theory in general. Consider the following circuit:

enter image description here

I understand that the resistor will have a constant voltage of 1V across it as it takes the DC component of the input voltage source. The capacitor will take the AC part of the input voltage source (the 0.5V peak-peak signal).

There's my first question: How can there be 1V across the resistor and 0.5V peak-to-peak across the capacitor when both devices are in parallel? Don't they have the same voltage across them?

The second question is when the capacitor current goes negative, it's supplying current to somewhere -> where does it supply current to if top node is at same voltage?

I feel like I'm missing some basic rule here?

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I understand that the resistor will have a constant voltage of 1V across it as it takes the DC component of the input voltage source.

This is way off base.

We model an ideal resistor as able to respond to any applied voltage, whether DC or AC of any frequency.

If you want a resistor that only responds to the DC component of the applied voltage, you'd want to include a very large series inductance attached to that resistor.

There's my first question: How can there be 1V across the resistor and 0.5V peak-to-peak across the capacitor when both devices are in parallel? Don't they have the same voltage across them?

They have the same voltage across them.

1 V DC plus a 0.25 V 1 Hz sinusoid.

The second question is when the capacitor current goes negative, it's supplying current to somewhere -> where does it supply current to if top node is at same voltage?

In general it could supply current to either the resistor, the voltage source, or both.

There's no rule that the current through the voltage source must always flow out the positive terminal.

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  • \$\begingroup\$ What about if I had a very large frequency AC signal on my voltage source. Shouldn't the capacitor then behave as a short, acting as a decoupling/bypass capacitor and then the resistor should only see the DC 1V? But then wouldn't that contradict the fact that resistor and capacitor should have same voltage across them? \$\endgroup\$ – AlfroJang80 Sep 20 at 16:02
  • \$\begingroup\$ @AlfroJang80, if you want to include that effect, you need to include a source impedance in your voltage source model. With the ideal voltage source you've drawn, the capacitor is never close enough to a short to prevent the resistor from seeing the full voltage. \$\endgroup\$ – The Photon Sep 20 at 16:03
  • \$\begingroup\$ May I ask why a source impedance is necessary? I thought the capacitor has an impedance of 1/jwC when dealing with sinusodial voltages and currents. \$\endgroup\$ – AlfroJang80 Sep 20 at 16:09
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    \$\begingroup\$ Yes, but an ideal voltage source can supply as much current as needed to drive it with 0.25 V AC. The ideal source can provide 1,000,000,000,000,000 amps if necessary to deliver the 0.25 V. If you want a source that will fail to deliver enough current to keep the AC voltage at 0.25 V at some high frequency, you need to include a source impedance in the voltage source model. \$\endgroup\$ – The Photon Sep 20 at 16:11
  • \$\begingroup\$ Ah. I see. Thank you \$\endgroup\$ – AlfroJang80 Sep 20 at 16:13
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The basic rule of lumped-circuit analysis is that parallel components all have the same voltage across them, and series components all have the same current flowing through them.

Your circuit is a parallel circuit, so the first rule applies. The voltage is strictly determined by the voltage source. The thing that's different is the current that flows in each component.

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