Answer:
a) Z = 85.9 ohms
b) 0.74 A
c) 37.1 W
Explanation:
Given : 90 sin (350 t )
Angular frequency = ω = 350 rad/s
C = 25 mF = 25 x 10⁻³ F
Inductance = L = 0.20 H
a) Inductive reactance = X(L) = ω L = (350)(0.2) = 70 ohms
Capacitive reactance = X(C) = 1 / ωC = 0.114 ohms
Reactance = Z = [tex]\sqrt{R^{2}+ (X_{L}- X_{C})^{2}}[/tex]
= [tex]\sqrt{50^{2}+ ( 70 - 0.114)^{2}}[/tex]
= 85.9 ohms
b) current = I = 90 / 85.9 = 1.048 A
[tex]I_{rms}=[/tex] = 1.048 / [tex]\sqrt{2}[/tex] = 0.74 A
c) P = [tex]I_{rms}^{2}[/tex] R = (0.74)(50) = 37.1 W
