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 University
Basic 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
Basic Circuit Theory Chpter14 Problems Reference answers to Selected Problems 4(1+3s) 1:(a)4e;(b) 2:a)115s 5 s+21 (1.5+0.5)u(t)+6(1);(b) ),(2t1-cos2 3: e+2 e(cos t+ sin t)]u(t) 4:xt)=2e-1-2ey,y(t)=e 6:(b)( 7:(a)5x10 u(t)V; (b)4000e+cos 10t+ 2 sin 10t)u(t)V 8:4+5 9:(9e+2e-)u(t)A 0:2e+3eA(t>0). DaLian Maritime University
Basic Circuit Theory Chpter14 Problems Reference Answers to Selected Problems 1: (a) 4e ; (b) −3s s e s s 3 2 4(1 3 ) + − ; (c) 4e cos3. −3s 2: (a) 1+ 2 1.5 0.5 + + s s s , (1.5+0.5e ) u(t)+ −2t δ (t); (b) ) 4 2 1 2 ( 4 1 2 2 + + + − s s s s , 4 1 (2t+1-cos 2tsin 2t) u(t). 3: [e +2 e t (cos t + sin t)] u(t). −t 4: x(t)=2 e -2 e , y(t)= e . −2t −3t −3t 5: 20(e -2 e ). −4t −5t 6: (b) s s e s s e s s − − − + ) 1 1 ) ( 1 1 ( 2 2 3 2 . 7: (a) 5 u(t) V; (b) 4000(-e +cos 10t+ 2 sin 10t) u(t) V. t e 4 5 10 − × −5t 8: 4+5e A. −50t 9: (9e +2 e ) u(t) A. −t / 6 −2t 10: 2e +3e A (t > 0). −0.1t −0.25t DaLian Maritime University 2