Question No. 3-4: Solution: Using equation 3-15, a) i (wt) = Vm Z 2 Z = √ R² + (WL) ² sin (wt-0) + Vm (sin 0) e-wt/wr (12) + (377 (0.012) ⇒Σ 12.82 = wL 0-tan" (WL) = R = 377 (0.012) tan 12 Ө = wx = 0.361 Yad WL 3/8 R = => wr= 0.377 377 (0.012) 12 Scanned with CamScanner i (wt) = 13.2 sin (wt -0.361) + 4.67e-wt 10.377 B = 3.50 rad b) [avg = = 201 4.36A (numerical integration) c) Irms = 6.70 A (numerical integration) 2 P= It¼ms R = 2 ( (6.70) (12) P = 538 W P d) Pf = & ⇒ = S 538 (120) (6.70) Pf = 0.67 Question 3-8: Solution: a) i (wt) = Vm sin (wt-0) - Vdc Z + Ae-wt/wz R Scanned with CamScanner A= Vm A- (-1/2 sin (9-0)+ VA) = "/w e R Z = √ R² + (WL)² = √√(10)² + (377 (0.075) Z = 30.0 = ta = tan" (X/L) R +/377 (0.075) (377 (0.075)) ⇒ O= 1.23 rad wr= WL R = 377 (0.075) 10 » ωτ: 2.83 α = sin" Vdc Vm 100 => 24012 0.299 rad => 17.1° Scanned with CamScanner i (wt) = 11.3 sin (wt-1.23) -10+21.2e-wt/2.83 ↑ B = 3.94 rad => 226° => Lavy = 3.13A Pole = Vale Lavg (numerical integration) = (100) (3.13) Pole = 313 W b) Irms = 4.81A (numerical integration) 2 PR = Irms R Putting values PR = = 2 (4.81) (10) 231 W P c) pf= & S 313+231 (240) (4.81) →Pf = 0.472 = 47.2% Scanned with CamScanner Question No. 3-24: Solution: a) Vo = Vm (I+ cosα) 2ñ 120 12 (1+co (1 + Los 45°) 25 介 Vo = 46.1 V b) P= Vrms R 2 For Vrms, We know the formula Vyms = Vm 2 Putting Values, = 120 √2 2 Vins 80.98 NOW, P= (80.9) эр = 100 2 65.5W Sinza + π 25 0.785 1 - + sin (2 (0.785)) 2ñ K Scanned with CamScanner