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341h7 - M341 H7(S Zhang 3.7,4.1 1 EP 3.7 2 8 13(Electrical...

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M341 H7 (S. Zhang) 3.7,4.1. 1. EP § 3.7: 2, 8, 13 (Electrical circuits) ans: 2. Suppose that the switch is intially in position 2, but is thrown to position 1 at time t = 0, so that I (0) = 0 and E = 100 for t > 0. Find I ( t ) and show that I ( t ) 4 when t → ∞ . L = 5 H, R = 25Ω . E 1 2 R L ans: ( § 3.7:2) 5 I + 25 I = 100 I H = Ce - 5 t I P = A = 4 By initial condition, I = I H + I P = Ce - 5 t + 4 = - 4 e - 5 t + 4 4 . We can solve it as a first order linear equation. 3. Suppose that Q (0) = 0. Find Q ( t ) and I ( t ). What is the maximum chargeon the capacitor for t 0 and when does it occur? E ( t ) = 100 e - 5 t , R = 10 , C = 0 . 02 . E 1 R C ans: ( § 3.7:8) Q + 5 Q = 10 e - 5 t Q H = Ce - 5 t Q P = tAe - 5 t = t 10 e - 5 t By initial condition, Q = Ce - 5 t + t 10 e - 5 t = t 10 e - 5 t We can solve it as a first order linear equation. ρ = e 5 t I ( t ) = Q ( t ) = 10(1 - 5 t ) e - 5 t Q max occurs at first I ( t ) = 0. I ( t ) = Q ( t ) = 10(1 - 5 t ) e - 5 t = 0 , t = 1 5 Q max = Q ( 1 5 ) = 2 e 4. In an RLC circuit with input voltage E ( t ), find I s p ( t ) in the standard form. R = 20Ω , L = 5 H, C = 0 . 01 F ; E ( t ) = 200 cos 5 tV.

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