AC Power Triangle

**Strings (S _{i}P_{j}A_{jk}) = S_{7}P_{3}A_{32} Base Sequence = 12735 String Sequence = 12735 - 3 - 32 **

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Figure 8.14 shows a simple AC circuit. Figure 8.14(a) is the time domain circuit while figure 8.14(b) is its power triangle. Given that
v(t) = 16cosωt; i(t) = 4cos(ωt - π/6); and ω 377 rad/sec. Determine:

(a) The power factor, *pf*.

(b) The values of the real power P, the reactive power Q and the apparent power S of the power triangle.

**The string**:

S_{7}P_{3}A_{32} (Force - Push).
**The math**:

Pj Problem of interest is of type *force*. Power and energy problems are *force problems*. Electric power is a *force-push*.

(a) The power factor, *pf* = cosθ
= cos30 = √3/2.

The power factor, *pf* = 0 for a purely inductive or capacitive load.

The power factor, *pf* = 1 for a purely resistive load.
0 < *pf* < 1, for every other case.

(b) V_{rms} = 0.707(16) = 11.312

I_{rms} = 0.707(4) = 2.828

P = V_{rms}I_{rms}cos30
= (√3/2)(11.312)(2.828) = 27.7 Watts.

Q = V_{rms}I_{rms}sin30
= (1/2)(11.312)(2.828) = 15.995 VAR (volt-amperes-reactive)

S = V_{rms}I_{rms}
= (11.312)(2.828) = 31.990 VA (volt-amperes)
= 27.7 + j15.995.

The *point* **.** is a mathematical abstraction. It has negligible size and a great sense of position. Consequently, it is front and center in abstract existential reasoning.

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