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) F 1 (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)? t4? t4? 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 ?10 H1.0 ?10s v - + )(tvF20μ ?k10 )(ti 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 v ?3 A F4 )(5.2 tu H4 i + t = 0 ?9 ?2 H2 ?1 V110 H3 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 1: (a) 4e ; (b) s3? s e s s 3 2 )31(4 ? + ; (c) 4e cos3. s3? 2: (a) 1+ 2 5.05.1 + + ss s , (1.5+0.5e ) u(t)+ t2? )(tδ ; (b) ) 4 212 ( 4 1 22 + + ?+ s s ss , 4 1 (2t+1-cos 2t- sin 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 . t2? t3? t3? 5: 20(e -2 e ). t4? t5? 6: (b) ss e ss e ss ? +?? ) 11 () 11 ( 2 2 23 . 7: (a) 5 u(t) V; (b) 4000(-e +cos 10t+ 2 sin 10t) u(t) V. t e 54 10 ? × t5? 8: 4+5e A. t50? 9: (9e +2 e ) u(t) A. 6/t? t2? 10: 2e +3e A (t > 0). t1.0? t25.0? DaLian Maritime University 2