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When applying the law of addition of voltage in RC series circuit with alternating sinusoidal current, we notice that voltage across the generator is equal to the sum of the voltages across all other components . When the voltage of the generator is equal to that across the resistor , that eventually means that voltage across the capacitor is zero . But the voltage across the capacitor is equal to the anti derivative of the current multiplied by $1/C$ (inverse of the capacitance ) . But when we have that the voltage of capacitor is equal to zero doesn't that mean that current is zero, too?
there might be a certain idea or rule that I've missed, but I'm confused because this then means that current flowing through the circuit is zero too ( current is unique in series circuit )?

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  • $\begingroup$ The voltage and current through a capacitor in an A/C circuit are both varying sinusoidally in time. This means that for U.S. current at 60 Hz, the capacitor sees 0 voltage and 0 current 120 times per second, but there is a phase difference between these variables. $\endgroup$ – David White Jan 23 at 20:55
  • $\begingroup$ In addition to my last comment, you can't use a simple extrapolation of Ohm's Law for A/C circuits ... the fact that the polarity of the circuit is being driven sinusoidally introduces complexities that don't exist in DC circuits. $\endgroup$ – David White Jan 23 at 21:03
  • $\begingroup$ thanks :) maybe trying to relate or apply concepts that are used in dc circuits is the problem . $\endgroup$ – student 12 Jan 23 at 21:10
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But when we have that the voltage of capacitor is equal to zero doesn't that mean that current is zero, too?

No, a capacitor is governed by the rule

$$I = C\frac{dV}{dt}.$$

So when its current is zero, it doesn't tell you anything about what its voltage is, it only tells you the voltage is not changing.

Similarly, if you know the value of the voltage, it doesn't tell you anything about the current. To know the current you need to know how quickly the voltage is changing.

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