Resposta Exercícios Pares Cap 13

4) a) T = \frac{1}{200} = 5 ms b) T = \frac{1}{40 M} = 25 ms c) T = \frac{1}{20 K} = 50 \mu s d) T = \frac{1}{1} = 1 s 6) f = 1 kHz T = \frac{1}{1 k} = 1 ms Tempo para 5 ciclos: 5 \times 1 ms = 5 ms 10) a) 360° = 2 \pi radianos \frac{40°}{360°} = \frac{\theta}{2 \pi} \Rightarrow \theta = 0,698 rad \text{ ou } \theta = 0,222 \pi rad b) \theta = 1,047 rad c) \theta = 2,356 rad d) \theta = 2,967 rad 12) \omega = 2 \pi f \quad f = \frac{1}{T} a) f = \frac{1}{1,8} = 0,555 Hz \quad \omega = 2 \pi \times 0,555 = 3,49 rad/s b) f = \frac{1}{0,3 \times 10^{-3}} = 3333,33 Hz \omega = 2 \pi \times 3333,33 = 20943,95 rad/s c) f = \frac{1}{8 \times 10^{-6}} = 125 kHz \omega = 2 \pi \times 125 \times 10^3 = 785,4 K rad/s d) f = \frac{1}{4 \times 10^{-6}} = 250 kHz \omega = 2 \pi \times 250 \times 10^3 = 1570,8 K rad/s 14) a) \omega = 2 \pi f \quad \Rightarrow f = \frac{\omega}{2 \pi} a) f = \frac{754}{2 \pi} = 120 Hz \quad T = \frac{1}{f} = \frac{1}{120} = 8,33 ms b) f = \frac{12}{2 \pi} = 1,91 Hz \quad T = \frac{1}{1,91} = 523,6 ms c) f = \frac{6000}{2 \pi} = 954,93 Hz \quad T = \frac{1}{954,93} = 1,05 ms d) f = \frac{0,16}{2 \pi} = 25,5 mHz \quad T = \frac{1}{25,5 \times 10^{-3}} = 39,27 s 20) \omega = 157 rad/s \quad f = \frac{157}{2 \pi} = 24,98 Hz T = \frac{1}{24,98} = 40 ms \Rightarrow 1 ciclo Meio ciclo \Rightarrow 20 ms 26) \text{a) } 50 \sen (\omega t + 0°) \text{b) } 5 \sen (\omega t + 120°) \text{c) } 2 \cos (\omega t + 10°) \text{d) } -20 \sen (\omega t + 10°) 28) \omega = 2 \pi f = 2 \pi \times 1000 = 6283,2 rad/s v(t) = 120 \sen (6283,2 t - 80°) \mu V 48) f = 60 Hz => W = 2π x 60 = 376,99 ≃ 377 rad/s a) Vm = Vet x √2 = 4,8 x √2 = 6,78 V Valor rms é o mesmo que valor eficaz! v(t) = 6,79 Sen (377t) V b) Im = 50 x 10⁻³ x √2 = 70,7 mA i(t) = 70,7 Sen (377t) mA c) Vm = 2 x 10³ x √2 = 2,83 kV v(t) = 2183 Sen (377t) kV