Capacitors allow ac to pass through them. But a capacitor is basically two conducting plates with a dielectric between them, right? And dielectrics are insulators. And as far as I know, there are no mechanical connections between the plates. So doesn't that mean there would be a discontinuity of circuit and current cannot flow in it, if a capacitor is present? Can you please explain?
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You are right about the structure of a capacitor and that there are no mechanical connections between the plates of a capacitor. You are also correct in saying that current cannot flow through the dielectric. What happens is that when there is a potential difference across the two plates, one plate will induce an equal and opposite charge on the other plate.
Consider a DC first. When the current is a DC, the amount of charges induced increases and the capacitor is said to be charging. Due to the induction of charges on one plate, charges still move, thus producing a current. Therefore, during the charging process, charges move on both sides of the dielectric, just not through it. For the same dielectric of the same thickness and cross-sectional area, there is a maximum amount of charges which can reside on both plates for a given potential difference, i.e. maximum amount of charge a capacitor can store. When the capacitor is fully charged, the charges on both sides of the dielectric will stop moving.
Now, if the current is an AC, the direction of the current keeps changing. When the current starts flowing in one direction, the capacitor will be charged. Then, when the current changes direction, the capacitor will be discharged because the negative charges are being induced on the previously positive plate and vice versa. Therefore, the capacitor will never be fully charged in this case. Hence, the charges on both sides of the dielectric will keep moving, i.e. a current flows. This makes it appear as though the AC "passes through" the capacitors.
Consider a DC first. When the current is a DC, the amount of charges induced increases and the capacitor is said to be charging. Due to the induction of charges on one plate, charges still move, thus producing a current. Therefore, during the charging process, charges move on both sides of the dielectric, just not through it. For the same dielectric of the same thickness and cross-sectional area, there is a maximum amount of charges which can reside on both plates for a given potential difference, i.e. maximum amount of charge a capacitor can store. When the capacitor is fully charged, the charges on both sides of the dielectric will stop moving.
Now, if the current is an AC, the direction of the current keeps changing. When the current starts flowing in one direction, the capacitor will be charged. Then, when the current changes direction, the capacitor will be discharged because the negative charges are being induced on the previously positive plate and vice versa. Therefore, the capacitor will never be fully charged in this case. Hence, the charges on both sides of the dielectric will keep moving, i.e. a current flows. This makes it appear as though the AC "passes through" the capacitors.