Introductory Physics Volume Two
Introductory Physics Volume Two
Introductory Physics Volume Two
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6.8 Phasor Diagrams 125<br />
Theorem: Impedance: Capacitor<br />
In an AC circuit the amplitude of the voltage on a capacitor is<br />
proportional to the amplitude of the current flowing through the<br />
capacitor.<br />
V C0 = Z C I 0 with Z C ≡ 1<br />
ωC<br />
The impedance of an capacitor is Z C = 1<br />
ωC .<br />
The voltage on a capacitor reaches the peak value one quarter of a cycle<br />
after the current does. For this reason the voltage on a capacitor in an<br />
AC circuit is said to follow the current by a phase of 90 ◦ .<br />
§ 6.8 Phasor Diagrams<br />
This relationship between the leading and following phases is often<br />
represented in a phasor diagraph. As you may recall an oscillation can<br />
be thought of as the horizontal component of a circular motion. So we<br />
can represent the current or voltage in and AC circuit as the horizontal<br />
component of a circular motion.<br />
The current is represented as a vector with constant length I 0 that is<br />
rotating in the counter clockwise direction. The real physical current<br />
is the projection of this vector onto the horizontal (Re) axis.<br />
One thing that is very nice about the phasor representation is that<br />
it allows us to clearly represent in a diagram the phase relationship between<br />
different quantities. Let us take the leading phase of the inductor