Exercício 1-2023 1

29/05/2023, 08:11 atividade eletricidade aplicada - xx.jpg https://classroom.google.com/u/1/c/NTQzODU2Njc0MTU3/a/NTU0MTY3MzU0Mzg5/details 1/1 Atitude Qb1 R jXc R ≈ 75Ω C = 49pF Z = \frac{(R)(Xc)|90^°|}{R - jXc} \text{to eq. gcd} Xc = \frac{1}{j2πfC} a) f = 100Hz Xc = \frac{1}{j2π100.49x10^{-12}} => Xc = -j338,163x10^3Ω ∴ Z = \frac{75}{338,163x10^3}|90°| Z ≈ 75∠0° b) f = 10kHz Xc = \frac{1}{j2π10x10^3.49x10^{-12}} => Xc ≈ -j338,627x10^3Ω ∴ Z = \frac{75}{338,627x10^3}|-90°| Z ≈ 75∠-0,912° c) f = 100kHz Xc = \frac{1}{j2π100x10^3.49x10^{-12}} = -j33,8627x10^3 ∴ Z = \frac{75}{33,8627x10^3}|-90°| = 74,9988∠-0,912° Z ≈ 74,9988∠-0,912° d) f = 1MHz Xc = \frac{1}{j2π1x10^6.49x10^{-12}} = -j3,38627x10^3Ω ∴ Z = \frac{75}{3,38627x10^3}|-90°| Z ≈ 74,9838∠(-1,369°) e) f = 10MHz Xc = \frac{1}{j2π.10x10^6.49x10^{-12}} = -j338,6275Ω ∴ Z = \frac{75}{346,8366}|-99,511° Z ≈ 73,825∠-1,0489° Qb1 L R f R: L : jω: jωL Z = \frac{R + |90°|}{R + jωL} ∴ Z = \frac{R}{R + jωL} L = 500x10^{-3} R = 16Ω XL = jωL = j2πfL X L = j2πfL b) X L = j2 Z = \frac{16}{31.4159x10^3}•|90°| Z ≈ 15.979•2.916° c) f = 100kHz XL = j2π•100x10^3•500x10^{-3} Z = \frac{16.314,159x10^3|90°}{31.4159x10^3|89.999°} b) f = 1MHz XL = j2π•1x10^1•s500x10^{-3} Z = \frac{16.314159x10^2|90°}{3 .14159x10^6|89°} L ≈ 1610 ∴ Z = e) f = 160 ΓΗιΡ XL = j2π10x10^6•500x10^{-3} ∴ Z ≈ 161 < 0° => 1/90006° ∴ Z ≈ 40 Pois R << XL