1. Given the sinusoidal voltage 𝑣(𝑡) = 50 cos(30𝑡 + 10°) 𝑉, find: a. The amplitude Vm b. The period T c. The frequency f and d. 𝑣(𝑡) at 𝑡 = 10 𝑚𝑠 connected in parallel with a 1.25 H inductor. 9. What value of 𝜔 will cause the forced response, 𝑣0, in Figure 1 to be zero? 2. Evaluate these determinants: 10 + 𝑗6 2 − 𝑗3 | −1 + 𝑗 20∠ − 30° −4∠ − 10° b. | | 16∠0° 3∠ − 45° 1 − 𝑗 −𝑗 0 1 −𝑗 | c. | 𝑗 1 𝑗 1+𝑗 a. | −5 3. Combine the following sinusoidal functions into a single trigonometric expression: a. 𝑦 = 30 cos(200𝑡 − 160°) + 15 cos(200𝑡 + 70°) b. 𝑦 = 90 sin(50𝑡 − 20°) + 60 cos(200𝑡 − 70°) c. 𝑦 = 50 cos(5000𝑡 − 60°) + 25 sin(5000𝑡 + Figure 1 10. Find the current 𝑖𝑜 in the circuit shown in Figure 2 when: a. 𝜔 = 1 𝑟𝑎𝑑/𝑠 b. 𝜔 = 5 𝑟𝑎𝑑/𝑠 c. 𝜔 = 10 𝑟𝑎𝑑/𝑠 110°) − 75 cos(5000𝑡 − 30°) d. 𝑦 = 10 cos(𝜔𝑡 + 30°) + 10 sin 𝜔𝑡 + 10 cos(𝜔𝑡 + 150°) 4. Evaluate the following: a. 3 cos(20𝑡 + 10°) − 5cos(20𝑡 − 30°) b. 40 sin 50𝑡 + 30cos(50𝑡 − 45°) c. 20 sin 400𝑡 + 10cos(400𝑡 + 60°) − 5 sin(400𝑡 − 20°) Figure 2 11. If 𝑖𝑠 = 5 cos(10𝑡 + 40°)𝐴 in the circuit of Figure 3, find 𝑖𝑜. 5. Two voltages 𝑣1 and 𝑣2 appear in series so that their sum is 𝑣 = 𝑣1 + 𝑣2. If 𝑣1 = 10 cos(50𝑡 − 𝜋⁄3)𝑉 and 𝑣2 = 12 cos(50𝑡 + 30°)𝑉, find 𝑣. 6. An alternating voltage is given by 𝑣(𝑡) = 55 cos(5𝑡 + 45°)𝑉. Use phasors to 𝑡 𝑑𝑣 find 10𝑣(𝑡) + 4 − 2 ∫ 𝑣(𝑡)𝑑𝑡. Assume that 12. Find 𝑣 (𝑡) in the circuit of Figure the value of the integral is zero at 𝑡 = −∞. 4 if the current 𝑖𝑥 through the 1-Ω resistor is 0.5 sin 200𝑡 𝐴. 𝑑𝑡 −∞ Figure 3 𝑠 7. Find 𝑣(𝑡) in the following integrodifferential equations using the phasor approach: a. 𝑣(𝑡) + ∫ 𝑣 𝑑𝑡 = 10 cos 𝑡 b. 𝑑𝑣 + 5𝑣(𝑡) + 4 ∫ 𝑣 𝑑𝑡 = 20 sin(4𝑡 + 10°) 𝑑𝑡 8. Find the values of resistance and inductance that when connected in series will have the same impedance at 4 krad/s as that of a 5 kΩ resistor Figure 4 13. Find 𝑣𝐴(𝑡) in Figure 5. Figure 5 14. The phasor current Ib in the circuit shown in Figure 6 is 25∠0° 𝑚𝐴. a. Find Ia, Ic, and Ig. b. If 𝜔 = 1500 𝑟𝑎𝑑/𝑠, write expressions for 𝑖𝑎(𝑡), 𝑖𝑏(𝑡), and 𝑖𝑔(𝑡). Figure 6 15. Calculate the value of 𝑍𝑎𝑏 in the network of Figure 7. Figure 7