Question

15. (15 Points) For the following RMS voltage and current, answer the following questions: Voltage is given by v(t) = 12 cos(2t +30°) Current is i(t) = 4 cos (2t +10°) a. What is the Average power? b. What are the Phasors of each? c. What is the Complex Power? d. What is the Reactive Power? e. What is the Power Factor? BONUS 1. (5 Points) If an AC circuit has a current lagging the voltage, what type of circuit is it? 2. (5 Points) If an AC circuit has a current that is leading the voltage, what type of circuit is it? 3. (5 Points) If an AC circuit has a current that is in-line with the voltage, what type of circuit is it?

Answer 1

Solutions- ult). ilt) = 12 cos (2t+30) = 4cos (24710) = 12 (30° V 4 (10° v a) Average Power, po vlt) x ilt) Ps 12 cos (2++36) x 4605 (27+10) = 48 cos ( 24+36) cos (2+10) = 24/2 cos (2++30°) cos (24710)] cos (A-B) As we know OCA COSR = cos (A+B) + then po 24/4s (2+ +30 +2+ +10°) + 603 (2++30 - 27-16)] +34 [cos ( 46 +40) + 65 (20)} [p = 24 cos (46146) + 22.55 wr Phasor of ult) = 30° phasor of ilt) = 10° ♡ ✓

complex Power (s) = vi* Sa 12 (30° x 4 1-10 s= 48/20 Sz 48 cos (2t +20) VA AS, - s = 48/20 = 45. 105 + 116.416 As we know S = Peja jQ= j 16-416 [Q2 16• 416 VAR 7 ASS= 48/26 power factor 0 2 20°

AS, i) If current lagging voltage theu circuit is inductive . current is leading the voltage then circuit is conductive ") of zen in f current is in eine voltagen then circuit is resislive.