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# ACexamples - ECE225 AC CIRCUIT EXAMPLES FALL 2009 Example 1...

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ECE225 AC CIRCUIT EXAMPLES FALL 2009 Example 1 v(t)=100 2 cos 120 t V + - 384 W 0.96 pf lag + - V ~ Z _ I ~ i(t) π (a) Find the power factor angle φ (deg). (b) Find the real power P (W), the reactive power Q (VAr), and the apparent power S (VA). (c) Find the complex power ¯ S (VA) in both rectangular and polar forms. (d) Check that ¯ S = | ¯ S | 6 φ where | ¯ S | = S . (e) Find the rms voltage phasor ˜ V (V). (f) Find the rms current phasor ˜ I (A). (g) Find the impedance ¯ Z (Ω) of the load in both polar and rectangular forms. (h) Check that ¯ Z = | ˜ V | / | ˜ I | 6 φ . (i) Check that ¯ S = ˜ V ˜ I * . (j) Check that ¯ S = ¯ Z | ˜ I | 2 = R | ˜ I | 2 + jX | ˜ I | 2 = P+jQ. (k) Find the instantaneous current i ( t ) (A). (l) Find the instantaneous power p ( t ) (VA). 1

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Example 1 – Solutions v(t)=100 2 cos 120 t V + - 384 W 0.96 pf lag + - V ~ Z _ I ~ i(t) π (a) φ = +cos - 1 pf = + cos - 1 0 . 96 = + 16 . 26 o (b) P = 384 W S = P cos φ = P pf = 384 0 . 96 = 400 VA Q = + p
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ACexamples - ECE225 AC CIRCUIT EXAMPLES FALL 2009 Example 1...

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