Basic Circuit Theory Chpter4 Problems 1 If the voltage across a 5F capacitor is 2te -V, find the current and the power 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 I(mA t (us) Fig 4-20 For prob. 3. 4 A 25 u 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 i(mA 20 Fig. 4-21 For prob. 4 5 (a)If the capacitor shown in Fig. 4-22 has a capacitance of 0. 2 u F, let v=5+3cos" 200t V, and find i, (t).(b)What is the maximum energy stored in the capacitor? 。 Fig. 4-22 For prob 6 If the current waveform in Fig. 4-23 is applied to a 20 u F capacitor, find the voltage v(t) across the capacitance. Assume the v(00 (1) Fig 4-23 For prob. 6 7 A voltage of 60cos4 Tt 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 eg 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
Basic Circuit Theory Chpter4 Problems 1 If the voltage across a 5F capacitor is 2te V, find the current and the power. −3t 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 = 2.5 µ s. Fig. 4-20 For prob. 3. t (mA ) 10 0 i − 5 − 10 5 2 4 6 (µ s) 4 A 25 µ 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 (µs) 10 20 20 30 Fig. 4-21 For prob. 4. 5 (a) If the capacitor shown in Fig.4-22 has a capacitance of 0.2 µ 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 20 µ 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 I nF 4 nF Fig. 4-24 For prob. 8. 9 Determine the equivalent capacitance of the network in Fig. 4-25 if all capacitors are 10u F Fig. 4-25 For prob. 9 0 Determine the equivalent capacitance of the circuit in Fig. 4-26 3F6F F Fig. 4-26 For prob. 10 11 For the circuit in Fig. 4-27, determine: (a)the voltage across each capacitor,(b)the energy stored in each "2F 90V+30F+14uF+80uF Fig. 4-27 For prob. 11 2 extend the concept of A-Y transformation to obtain the equivalent capacitance of the network shown in Fig 4-28 50HF 30u F 10u F Fig. 4-28 For prob. 12 DaLian Maritime University
Basic Circuit Theory Chpter4 Problems 2 nF 4 nF 1 nF 2 nF a b C eq 9 Determine the equivalent capacitance of the network in Fig.4-25 if all capacitors are 10 µ 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. 2 F 3 F 3 F 4 F 6 F 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. + - 30µF 60µF 80µF 20µF V 14µF 90 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. 30µF 50µF 10µ F 20µF 40µF DaLian Maritime University 2
Basic Circuit Theory Chpter4 Problems Reference answers to Selected Problems 1:10(1-3teA,20t(1-3teW 2:0.48A 3:p=3W 4:(a)96V,192mW,1152mJ;(b)l6V,oW,3.2mJ 5:(a)-0.12sin400tmA(b)644J,(c)400(1-e-yv;(d)500-400c-y 6:=100t2kV0<t<1,v=1004-t2-2)kv1<t<2 7:-0.72丌sin4丌tA,-5.4J 8:2.4nF 9:4.286F 0:(a)3F;(b)8F;(c)lF 11:(a)V=90V,V6o=60V,V14=60VV20=48V,Vo=12v (b)Wso=1215mJ,W6o=27m,W14=252mJ,W20=2304mJ,Wso=5.76mJ 12:22.39HF DaLian Maritime University
Basic Circuit Theory Chpter4 Problems Reference Answers to Selected Problems 1: 10(1-3t)e A, 20t(1-3t)e W. −3t −6t 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) 6.4 µ J; (c) 400(1–e )V; (d) 500-400e V −100t −100t 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: 4.286 µ F. 10: (a) 3F; (b) 8F; (c) 1F. 11: (a) V =90V, V =60V, V14 =60V, V =48V, V =12V; 30 60 20 80 (b) W =121.5 mJ, W =27 mJ, W14 =25.2 mJ, W =23.04 mJ, W =5.76 mJ. 30 60 20 80 12: 22.39 µ F. DaLian Maritime University 3