Notes_ACPwr_Ex_S07.pdf - ECE 2210 AC Power Examples A.Stolp rev Ex 1 R L together are the load Find the real power P the reactive power Q the complex

Notes_ACPwr_Ex_S07.pdf - ECE 2210 AC Power Examples A.Stolp...

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A.Stolp 11/06/02 rev 2/27/07 ECE 2210 AC Power Examples Ex. 1 R & L together are the load. Find the real power P , the reactive power Q , the complex power S , the apparent power | S |, & the power factor pf . Draw phasor diagram for the power. V in . 110 V R . 10 Ω L . 25 mH Z 1 1 R 1 . . j ω L = 1 . . 0.1458 1 Ω e . . j 46.7 deg ω . 377 rad sec load = Z 4.704 + 4.991j Ω = Z 6.859 Ω θ arg ( ) Z = θ 46.7 deg pf cos ( ) θ = pf 0.686 I V in Z = I 11 11.671j A = I 16.038 A = arg ( ) I 46.7 deg P . . V in I pf = P 1.21 kW Q . . V in I sin ( ) θ = Q 1.284 kVAR OR... Q . . V in I 1 2 pf 2 = Q 1.284 kVAR S . V in I OR.. S P . j Q = S 1.21 + 1.284j kVA S Re ( ) S 2 Im ( ) S 2 = = S 1.764 kVA = atan Im ( ) S Re ( ) S 46.696 deg S = 1.764kVA /46.7 o OR, since we know that the voltage across each element of the load is V in ... Real power is dissipated only by resistors P V in 2 R = P 1.21 kW Q V in 2 . ω L = Q 1.284 kVAR S P . j Q S = S = = P 2 Q 2 1.764 kVA pf = = P S 0.686 What value of C in parallel with R & L would make pf = 1 ( Q = 0 ) ? = Im ( ) I 11.671 A X C V in Im ( ) I = X C 9.425 Ω = 1 . ω C = 1 . X C ω 281 μ F OR.. ω = 1 . L C C 1 . L ω 2 = C 281 μ F Ex. 2 R & L together are the load. Find the real power P , the reactive power Q , the complex power S , the apparent power | S |, & the power factor pf . Draw phasor diagram for the power. Series R & L R . 10 Ω Z R . . j ω L V in . 110 V load = Z 10 + 9.425j Ω = Z 13.742 Ω ω . 377 rad sec L . 25 mH θ arg ( ) Z = θ 43.304 deg pf cos ( ) θ = pf 0.728 I V in Z = I 5.825 5.49j A = I 8.005 A = arg ( ) I 43.304 deg P . . V in I pf = P 0.641 kW Q . . V in I sin ( ) θ = Q 0.604 kVAR S . V in I = S 0.641 + 0.604j kVA = S 0.881 kVA = arg ( ) S 43.304 deg S = 881VA /43.3 o ECE 2210 AC Power Examples, p.1
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ECE 2210 AC Power Examples, p.2 OR, if we first find the magnitude of the current which flows through each element of the load...
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