Question

Problem 4 (20pts). A transformer with N1, N3 turns at the input and N2, N4 turns at the output is wrapped as drawn. The magnetic flux in the core is given as Q = -20sin(wt) (Wb), and R, = 1k.. Find: a) V2 V3 and 12, 13. b) Direction of 12, 13. c) What is Rin? N=600 N2=300 Nz=100 N=300 12 13 Rin RL V V2 V3 R -100082

Answer 1

0 $=-80 Sinwt) Nido to dt V3 6x103 coswt Ny dd 300 d (zesinwt) dt - 6x103 osfwt) 21TX 60 w=2 TTT Assume frequency f= 60Hz V3 = -6x 103 coswt gif V2 --15.915 ws (wt) V = Ny =) V₂ = V3 (N3) = V (loon N3 V = 1615.915) cos (wt) -5.305 cos(wt) V2 - 3 = -15.915 Lo swt ma A Iz = V₂ = -15.915 coswt RL 1x103 Iz N3 100 I. = -15.91543 oswt mA Iq Ny 300 Ta 47.745 Co swt mA b) Direction of Iz is clockwise Direction af I is clock wise c) Il = N2 =) I = 300 x 47.745 cos wť m A) Ig loo I1 =-143.23560 Swt mA

V2 300 c V = Ni =) y = boo (-5:305 ws{wt)) N₂ V-10.61.coswt = -10.6120 = -143.245 Z0 mA Rin t0.67 X1000 -T43,245 = 740068 Rin=74.068 r