Basic Circuit Theory Chpter14 Problems I Find F(s) if f(t)=:(a)40(t-3); (b)4t u(t-3); (c)4 cos to(t-3) 2 Obtain partial-fraction expansions for each of the following rational functions, and find the corresponding time functions (a)F1(s)=[(s+1)s+3)/S(s+2)l (b)F2(s)=(s+2)s2(s2+4) 3 Expand(3s+)(s+1)(s -2s+2) by partial fraction and then determine its inverse Laplace transfor 4 Solve the following set of differential equations for the functions x(t)and y(t) using the Laplace ansform technique: 2x'+ 4x+y'-y=0, X'+2x +y'+y=0, where x(0-0 and y(oFl 5 It is known that the impulse response of a linear system is 5e u(t), What output is produced by the input 4e u(t)? 6 Given the signals f, (t)=tlu(t+2)-u(t-1)] and f,(t)=u(t-3):(a) work in the time domain to find f, (t)*f2(t: (b)find E(f, (t)*f2(t)] 7 Find v(t)for the circuit illustrated in Fig. 14-15 ifis(t)=(a)8(t); (b)2cos 10t u(t) 10k9220Fv( 109 0.1H Fig. 14-15 For prob. 7. Fig. 14-16 For prob. 8 8 In the circuit shown in Fig. 14-16, let vs(t)=50u(t)+28(t)-10 V, use Laplace transform methods to find i(t) for t>0 9 Draw a frequency-domain equivalent for the circuit shown in Fig. 14-17 that is valid for t>0 and then find i(t) 99 士110v 25u(1)AA 3/4F 4H5291 Fig. 14-17 For prob. 9. Fig. 14-18 For prob. 10 10 Let 1(0 )=2V and i(0 )=5A in the circuit of Fig 14-18. Find i(t) for t>0 DaLian Maritime UniversityBasic Circuit Theory Chpter14 Problems 1 Find F(s) if f(t) = : (a) 4δ (t - 3); (b) 4t u(t – 3); (c) 4 cos tδ (t - 3). 2 Obtain partial-fraction expansions for each of the following rational functions, and find the corresponding time functions: (a) F1 (s) = [(s+1)(s+3)]/[s(s+2)]; (b) F (s) = (s+2)/[s (s +4)]. 2 2 2 3 Expand (3s 2 +2)/[(s+1)(s -2s+2)] by partial fraction and then determine its inverse Laplace transform. 2 4 Solve the following set of differential equations for the functions x(t) and y(t) using the Laplace transform technique: 2x’+ 4x + y’- y =0, x’+2x +y’ +y = 0, where x(0)=0 and y(0)=1. 5 It is known that the impulse response of a linear system is 5e u(t), What output is produced by the input 4e u(t)? −4t −4t 6 Given the signals f 1 (t) = t[u(t+2)-u(t-1)] and f (t) = u(t-3): (a) work in the time domain to find f (t) f (t); (b) find £[f 1 (t)∗ f 2 (t)]. 2 1 ∗ 2 7 Find v(t) for the circuit illustrated in Fig. 14-15 if i (t) =: (a) S δ (t); (b) 2cos 10t u(t). + - i 10Ω s 10Ω 0.1H v - + 20µF v(t) 10kΩ i (t) s Fig. 14-15 For prob. 7. Fig. 14-16 For prob. 8. 8 In the circuit shown in Fig. 14-16, let v (t) = 50u(t) + 2 S δ (t) – 10 V, use Laplace transform methods to find i(t) for t > 0. 9 Draw a frequency-domain equivalent for the circuit shown in Fig. 14-17 that is valid for t > 0 and then find i(t). 2 Ω v 3 Ω A 4F 2.5u(t) 4H i + t =0 9Ω 2 Ω 2H 1Ω 110V 3H i Fig. 14-18 For prob. 10. Fig. 14-17 For prob. 9. 10 Let v(0 ) = 2V and i(0 ) =5A in the circuit of Fig. 14-18. Find i(t) for t > 0. − − DaLian Maritime University 1