twometer - ECE225 TWO-WATTMETER METHOD UNBALANCED CASE...

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ECE225 TWO-WATTMETER METHOD – UNBALANCED CASE SPRING 2008 - a b c A B C b B C c a A I CA + - bn 10 j10 -j10 ~ ~ ~ Z ~ o V =127 0 V o V =127 120 V ~ I cC bB I ~ aA I ~ an AB I ~ BC I ~ CA n N ca o V =127 -120 V cn - Z BC - Z AB - - + + - + - V V bc ab V + - + (a) Find ˜ V AB , ˜ V BC , and ˜ V CA geometrically. ˜ V AB = ˜ V ab = ˜ V BC = ˜ V bc = ˜ V CA = ˜ V ca = (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 = ¯ Z BC = ¯ Z A ¯ Z B + ¯ Z B ¯ Z C + ¯ Z C ¯ Z A ¯ Z A = ¯ Z CA = ¯ Z A ¯ Z B + ¯ Z B ¯ Z C + ¯ Z C ¯ Z A ¯ Z B = (c) Find P 3 φ . P 3 φ = (d) Find Q 3 φ . Q 3 φ = 1
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(e) Find ˜ I AB , ˜ I BC , and ˜ I CA in polar and rectangular coordinates. ˜ I AB = ˜ V AB ¯ Z AB = ˜ I BC = ˜ V BC ¯ Z BC = ˜ I CA = ˜ V CA ¯ Z CA = (f) Find ˜ I aA , ˜ I bB , and ˜ I cC in rectangular and polar coordinates. ˜ I
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twometer - ECE225 TWO-WATTMETER METHOD UNBALANCED CASE...

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