
AC Power Fundamentals 11
Then
à + B
˜
= (51.96 + 20) + j (30 + 34.64) = 71.96 + j 64.64 = 96.73 ∠41.93°
à – B
˜
= (51.96 – 20) + j (30 – 34.64) = 31.96 – j 4.64 = 32.30 ∠–8.26°
For multiplying and dividing, we must use à and B
˜
in θ-form as given, that is,
A × B
˜
= 60∠30° × 40∠60° = 60×40∠30+60 = 2400∠90° = 2400 (cos90 + j sin90) =
0 + j 2400
à / B
˜
= 60∠30° ÷ 40∠60° = (60 ÷ 40)∠30 – 60 = 1.5∠–30° = 1.5 (cos30 – sin30) =
1.3 – j 0.75
Example 1.4
Determine
2
1 5j .
in θ-form.
SOLUTION
All ac voltages, currents, impedances, and powers are phasors, that is, complex
numbers having x + j y components or the rms magnitude and phase angle θ.
When we write ...