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Physics LibreTexts

13.2: Alternating Voltage across a Capacitor

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At any time, the charge Q on the capacitor is related to the potential difference V across it by Q=CV. If there is a current in the circuit, then Q is changing, and I=C˙V.

13.3.png

FIGURE XIII.3

Now suppose that an alternating voltage given by

V=ˆVsinωt

is applied across the capacitor. In that case the current is

I=CωˆVcosωt,

which can be written

I=ˆIcosωt,

where the peak current is

ˆI=CωˆV

and, of course

IRMS=CωVRMS.

The quantity 1/(Cω) is called the capacitive reactance XC. It is expressed in ohms (check the dimensions), and, the higher the frequency, the smaller the reactance. (The frequency ν is ω/(2π).)

When we come to deal with complex numbers, in the next and future sections, we shall incorporate a sign into the reactance. We shall call the reactance of a capacitor 1/(Cω) rather than merely 1/(Cω), and the minus sign will indicate to us that V lags behind I. The reactance of an inductor will remain Lω, since V leads on I.

Comparison of equations ??? and ??? shows that the current and voltage are out of phase, and that V lags behind I by 90°, as shown in Figure XIII.4.

13.4.png

FIGURE XIII.4


This page titled 13.2: Alternating Voltage across a Capacitor is shared under a CC BY-NC 4.0 license and was authored, remixed, and/or curated by Jeremy Tatum via source content that was edited to the style and standards of the LibreTexts platform.

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