Basic Circuit Theory Chpter6 Problems 1 Let L = 1.25 H in Fig.6-11, and determine v(t) if v(0 ) = 100 V and: (a) i C (0 ) = 20A; (b) i (0 ) = 20A. + + L + - + ?2 L L i C i R i F05.0 v Fig. 6-11 For prob. 1 . 2 (a) What value of L in the circuit of Fig.6-11 will result in a transient response of the form, v(t) = Ae + Be？A 4 t4? t6? 3 Element values in the circuit of Fig.6-12 are : v = 100V, R = 10 S S ? , L = 2mH, and C = 20/3μ F. The switch closes at t = 0, find v (t) R 4 A 4μ F capacitor and a 10mH inductor are used in a critically damped parallel RLC circuit. (a) Find R resistor. (b) At t = 0 the capacitor voltage is 100V and it is absorbing 50W, write the response of the capacitor voltage versus t. t =0 -+ - + C s R L R R v s v Fig. 6-12 For prob.4. 5 The switch in Fig.6-13 has been closed for hours. It is opened at t = 0, show that a 10V battery can be a lethal weapon by finding v at t = 2.5π μ s. - t=0 + v nF10 mH5.2 V10 ?5.0 Fig. 6-13 For prob.5. 6 For the circuit shown in Fig.6-14, find v (t) and i (t). C C + -- + V ?1200 C i C v )(tu F 3 10 μ 50 V20 H20 Fig. 6-14 For prob.6. DaLian Maritime University 1 Basic Circuit Theory Chpter6 Problems 7 For the circuit shown in Fig.6-15, find v (t) and i (t). C L - + A ?25 L i F25μ C v )(53 tu? mH5.2 8 The strength of the current source in Fig.6-16 is suddenly increased from 10A to 20A at t = 0, find v (0 ), v (0 ), v ( ), and v (t). S ? S + S ∞ S Fig. 6-15 For prob.7. - + H1 s v ?3 ?2 mF80 A10 Fig. 6-16 For prob.8. 9 A source-free parallel RLC circuit contains an inductor for which the product 0 ω L is 10 . If s 1 = - 6s and s 2 = - 8s , find R, L, and C. ? 1? 1? 10. With reference to the circuit of Fig.6-17, let i(0) = 40A and v(0) = 40V. If L = 12.5H, R = 0.1? , and C = 0.2F, find v(t) R CL C iR ii v ? + Fig. 6-17 For prob.10. Reference Answers to Selected Problems 1: (a) 200e -100e V (t >0); (b) -100e +200e V ( t > 0). t2? t8? t2? t8? 2: (a) 5/6 H; (b) v(t)=210e -190e V (t > 0). t4? t6? 3: 200(e - e ). t5000? t15000? 4: (a) 25 ; (b) (100+6.25t) e V (t > 0). ? t5000? 5: -9992V. 6: 20+250(e -e )V, t100? t150? 24 1 (3e -2 e )A. t150? t100? 7: (a) –50+ 3 25 (16e -e )V (t >0); (b) –2+ t2000? t8000? 3 5 (4 e -e ) (t >0). t2000? t8000? 8: (a) 20V; (b) 50V;(c) 40V; (d)40+e (10 cos 2.5t+24 sin 2.5t)V (t>0). t5.2? 9: 4.95? , 1.443H, 14.43 mF. 10: (a) –20e +60e V (t >0). t10? t40? DaLian Maritime University 2