19.5. Alternating Current Applications
19.5.1. Rotating Vectors in the Complex Plane
We have already shown that a vector can be represented by a complex number. For example, the complex number 
represents a vector of magnitude 5.00 at an angle of 28° with the real axis.
|
Glance back to Chap. 15 where we first introduced alternating current. |
A phasor (a rotating vector) may also be represented by a complex number 
by replacing the angle θ by ωt where ω is the angular velocity and t is time.
Example 32:The complex number
represents a phasor of magnitude 11 rotating with an angular velocity of 5 rad/s. |
Figure 19.12. FIGURE 19-12
In Sec. 15–3 we showed that a phasor of magnitude R has a projection on the y axis of R sin ωt. Similarly, a phasor 
in the complex plane (Fig. 19-12) will have a projection on the imaginary axis of R sin ωt. Thus
Similarly,
Thus either a sine or a cosine wave ...
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