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stwometer

# stwometer - ECE225 TWO-WATTMETER METHOD UNBALANCED CASE...

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ECE225 TWO-WATTMETER METHOD – UNBALANCED CASE SPRING 2008 AB I ~ BC I ~ CA n N ca o an o ~ ~ a b c A B C b B C c a A I 10 V bc ~ 220 30 o V =127 0 VAC VAC cn o V =127 120 V =127 -120 VAC V = j10 -j10 ~ I bB ~ I aA ~ I cC ab ~ + - V + - + - + - bn 10 j10 -j10 - - + + (a) Find ˜ V AB , ˜ V BC , and ˜ V CA geometrically. ˜ V AB = ˜ V ab = 127 3 6 30 o = 220 6 30 o V(rms) ˜ V BC = ˜ V bc = 127 3 6 - 90 o = 220 6 - 90 o V(rms) ˜ V CA = ˜ V ca = 127 3 6 150 o = 220 6 150 o V(rms) (b) Find ¯ Z AB , ¯ Z BC , and ¯ Z CA using the Y-to-∆ transformation: ¯ Z AB = ¯ Z A ¯ Z B + ¯ Z B ¯ Z C + ¯ Z C ¯ Z A ¯ Z C = (10)( - j 10) + ( - j 10)( j 10) + ( j 10)(10) j 10 = - j 10 Ω ¯ Z BC = ¯ Z A ¯ Z B + ¯ Z B ¯ Z C + ¯ Z C ¯ Z A ¯ Z A = (10)( - j 10) + ( - j 10)( j 10) + ( j 10)(10) 10 = 10 Ω ¯ Z CA = ¯ Z A ¯ Z B + ¯ Z B ¯ Z C + ¯ Z C ¯ Z A ¯ Z B = (10)( - j 10) + ( - j 10)( j 10) + ( j 10)(10) - j 10 = j 10 Ω (c) Find P 3 φ . P 3 φ = | ˜ V BC | 2 R BC = 220 2 10 = 4840 W (d) Find Q 3 φ . Q 3 φ = | ˜ V AB | 2 X AB + | ˜ V CA | 2 X CA = 220 2 - 10 + 220 2 10 = 0 VAr 1

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(e) Find ˜ I AB , ˜ I BC , and ˜ I CA in polar and rectangular coordinates.
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stwometer - ECE225 TWO-WATTMETER METHOD UNBALANCED CASE...

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