Basic Circuit Theory Chpter4 Problems 1 If the voltage across a 5F capacitor is 2te V, find the current and the power. t3? 2 In 5s, the voltage across a 40mF capacitor changes from 160V to 220V. Calculating the average current through the capacitor. 3 The current in a 50pF capacitor is given by the waveform of Fig.4-20. Sketch a curve of the power being delivered to the capacitor as a function of time and determine the value of p at t = 2.5μ s. Fig. 4-20 For prob. 3. t )mA( 10 0 i 5? 10? 5 246 )s(μ 4 A 25μ F capacitor having no voltage across it at t = 0 is subjected to the single pulse of current shown in Fig.4-21. Determine the voltage across, the power entering, and the energy stored in C at t =: (a) 17ms; (b) 40ms. t )mA( 10 0 i )( sμ 10 20 20 30 Fig. 4-21 For prob. 4. 5 (a) If the capacitor shown in Fig.4-22 has a capacitance of 0.2μ F, let v = 5 + 3cos 2 200t V, and find i (t). (b) What is the maximum energy stored in the capacitor? c c + - i C v Fig. 4-22 For prob. 6 If the current waveform in Fig.4-23 is applied to a 20μ F capacitor, find the voltage v(t) across the capacitance. Assume the v(0)=0. t )(t 0 i 2 4 1 Fig. 4-23 For prob. 6. 7 A voltage of 60cos4π t V appears across the terminals of 0.3mF capacitor. Calculate the current through the capacitor and the energy stored in it from t=0 to t=0.125s. 8 Find C eq for the lattice network shown in Fig.4-24, if terminals a and b are: (a) open-circuited as shown; (b) short-circuited. DaLian Maritime University 1 Basic Circuit Theory Chpter4 Problems nF2 nF4 nF1 nF2 a b eq C 9 Determine the equivalent capacitance of the network in Fig.4-25 if all capacitors are 10μ F. Fig. 4-24 For prob. 8. 10 Determine the equivalent capacitance of the circuit in Fig.4-26 Fig. 4-25 For prob. 9. F2 F3 F3 F4 F6 11 For the circuit in Fig.4-27, determine: (a) the voltage across each capacitor, (b) the energy stored in each capacitor. Fig. 4-26 For prob. 10. + - F30μ F60μ F80μ F20μ F14μ V90 Fig. 4-27 For prob. 11. 12 extend the concept of transformation to obtain the equivalent capacitance of the network shown in Fig.4-28. Υ?? Fig. 4-28 For prob. 12. F30μ F50μ F20μ F10μ F40μ DaLian Maritime University 2 Basic Circuit Theory Chpter4 Problems Reference Answers to Selected Problems 1: 10(1-3t)e A, 20t(1-3t)e W. t3? t6? 2: 0.48A 3: p=3W. 4: (a) 9.6V, 192 mW, 1.152 mJ; (b) 16V, 0W, 3.2 mJ. 5: (a) –0.12 sin 400t mA;(b) 6.4μ J; (c) 400(1–e )V; (d) 500-400e V t100? t100? 6: v=100t kV 0 < t <1, v=100(4t- t -2) kV 1 < t <2. 2 2 7: - 0.72π sin 4π t A, - 5.4 J. 8: 2.4 nF. 9: 4.286μ F. 10: (a) 3F; (b) 8F; (c) 1F. 11: (a) V =90V, V =60V, V 14 =60V, V =48V, V =12V; 30 60 20 80 (b) W =121.5 mJ, W =27 mJ, W 14 =25.2 mJ, W =23.04 mJ, W =5.76 mJ. 30 60 20 80 12: 22.39 μ F. DaLian Maritime University 3