Problems. Figure 6.46 For Prob Figure 6.45 For Prob. 6.5.

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1 Prolems Section 6. pcitors 6.1 If the voltge cross 7.5-F cpcitor is find the current nd the power. te 3t V, 6. A 5-mF cpcitor hs energy w(t) 1 cos 377t J. Determine the current through the cpcitor. 6.3 Design prolem to help other students etter understnd how cpcitors work. 6. A current of sin t A flows through 5-F cpcitor. Find the voltge v(t) cross the cpcitor given tht v() 1 V. 6.5 The voltge cross -mf cpcitor is shown in Fig Find the current wveform. 6.6 The voltge wveform in Fig. 6.6 is pplied cross 55-mF cpcitor. Drw the current wveform through it. v(t) V 1 1 Figure 6.6 For Pro t (ms) v(t) V 1 1 Figure 6.5 For Pro t (ms) 6.7 At t, the voltge cross 5-mF cpcitor is 1 V. lculte the voltge cross the cpcitor for t 7 when current 5t ma flows through it. 6.8 A -mf cpcitor hs the terminl voltge v If the cpcitor hs n initil current of A, find: () the constnts A nd B, 5 V, t Ae 1t Be 6t V, t () the energy stored in the cpcitor t t, (c) the cpcitor current for t 7.

2 6.9 The current through.5-f cpcitor is 6(1 e t ) A Two cpcitors ( 5 mf nd 75 mf) re connected Determine the voltge nd power t t s. Assume to 1-V source. Find the energy stored in ech v(). cpcitor if they re connected in: 6.1 The voltge cross 5-mF cpcitor is shown in Fig Determine the current through the cpcitor. v (t) (V) 16 () prllel () series 6.16 The equivlent cpcitnce t terminls - in the circuit of Fig. 6.5 is 3 mf. lculte the vlue of. Figure 6.7 For Pro t ( s) 6.11 A -mf cpcitor hs the current wveform shown in Fig Assuming tht v() 1 V, sketch the voltge wveform v(t). i(t) (ma) Figure 6.8 For Pro t (s) Figure 6.5 For Pro F 8 F 6.17 Determine the equivlent cpcitnce for ech of the circuits of Fig F 5 F 3 F 6 F () 1 F 6 F F F F 6.1 A voltge of 3e t V ppers cross prllel comintion of 1-mF cpcitor nd 1- resistor. lculte the power sored y the prllel comintion. F () 3 F 6 F 6.13 Find the voltge cross the cpcitors in the circuit of Fig. 6.9 under dc conditions. F 3 F Ω Figure 6.9 For Pro Section Ω 5 Ω Ω 1 v 1 v 6 V Series nd Prllel pcitors Figure 6.51 For Pro (c) 6.18 Find eq in the circuit of Fig. 6.5 if ll cpcitors re mf. 6.1 Series-connected -pf nd 6-pF cpcitors re plced in prllel with series-connected 3-pF nd 7-pF cpcitors. Determine the equivlent cpcitnce. Figure 6.5 For Pro eq

3 6.19 Find the equivlent cpcitnce etween terminls nd in the circuit of Fig All cpcitnces re in mf. 8 F 1 F 1 F 35 F 5 F 1 F 15 F 15 F Figure 6.53 For Pro Find the equivlent cpcitnce t terminls - of the circuit in Fig Figure 6.56 For Pro Using Fig. 6.57, design prolem tht will help other students etter understnd how cpcitors work together when connected in series nd in prllel. 1 V 3 1 F 1 F Figure 6.57 For Pro F F F 6. For the circuit in Figure 6.58, determine () the voltge cross ech cpcitor nd () the energy stored in ech cpcitor. 6 F F 3 F 3 F 3 F 3 F 9 V 3 F 1 F 8 F Figure 6.5 For Pro. 6.. Figure 6.58 For Pro () Show tht the voltge-division rule for two cpcitors in series s in Fig. 6.59() is 6.1 Determine the equivlent cpcitnce t terminls - of the circuit in Fig F 6 F F v 1 1 v s, v 1 1 v s ssuming tht the initil conditions re zero. 1 Figure 6.55 For Pro F 3 F 1 F 6. Otin the equivlent cpcitnce of the circuit in Fig v s v 1 v () Figure 6.59 For Pro () i 1 i

4 () For two cpcitors in prllel s in Fig. 6.59(), show tht the current-division rule is i 1 1 1, i 1 ssuming tht the initil conditions re zero. 6.6 Three cpcitors, 1 5 mf, 1 mf, nd 3 mf, re connected in prllel cross 15-V source. Determine: () the totl cpcitnce, () the chrge on ech cpcitor, (c) the totl energy stored in the prllel comintion. 6.7 Given tht four -mf cpcitors cn e connected in series nd in prllel, find the minimum nd mximum vlues tht cn e otined y such series/prllel comintions. *6.8 Otin the equivlent cpcitnce of the network shown in Fig Assuming tht the cpcitors re initilly unchrged, find in the circuit of Fig v o (t) (ma) 9 1 Figure 6.6 For Pro t (s) 6 F 3 F v o (t) 6.31 If v(), find v(t), i 1 (t), nd i (t) in the circuit of Fig (ma) F 3 F 5 F t 1 F F 3 Figure 6.6 For Pro Determine eq for ech circuit in Fig i 1 6 F F i v Figure 6.63 For Pro eq () 6.3 In the circuit of Fig. 6.6, let 5e t ma nd v 1 () 5 V, v () V. Determine: () v 1 (t) nd v (t), () the energy in ech cpcitor t t.5 s. eq 1 F Figure 6.61 For Pro () v 1 F v F * An sterisk indictes chllenging prolem. Figure 6.6 For Pro. 6.3.

5 6.33 Otin the Thevenin equivlent t the terminls, -, of the circuit shown in Fig Plese note tht Thevenin equivlent circuits do not generlly exist for circuits involving cpcitors nd resistors. This is specil cse where the Thevenin equivlent circuit does exist. 6.1 The voltge cross -H inductor is (1 e t ) V. If the initil current through the inductor is.3 A, find the current nd the energy stored in the inductor t t 1 s. 6. If the voltge wveform in Fig is pplied cross the terminls of 5-H inductor, clculte the current through the inductor. Assume i() 1 A. 5 F v(t) (V) 5 V 1 Figure 6.65 For Pro F F Figure 6.67 For Pro t Section 6. Inductors 6.3 The current through 1-mH inductor is 1e t A. Find the voltge nd the power t t 3 s An inductor hs liner chnge in current from 5 ma to 1 ma in ms nd induces voltge of 16 mv. lculte the vlue of the inductor Design prolem to help other students etter understnd how inductors work The current through 1-mH inductor is sin 1t A. Find the voltge, cross the inductor for 6 t 6 p s, nd the energy stored t t p 6.38 The current through -mh inductor is i(t), t 6 te t A, t 7 Find the voltge v(t). s The voltge cross -mh inductor is given y v(t) 3t t V for t 7. Determine the current i(t) through the inductor. Assume tht i() 1 A. 6. The current through 5-mH inductor is shown in Fig Determine the voltge cross the inductor t t 1, 3, nd 5 ms. 6.3 The current in n 8-mH inductor increses from to 6 ma. How much energy is stored in the inductor? *6. A 1-mH inductor is connected in prllel with -k resistor. The current through the inductor is i(t) 5e t ma. () Find the voltge v cross the inductor. () Find the voltge v R cross the resistor. (c) Does v R (t) v (t)? (d) lculte the energy in the inductor t t. 6.5 If the voltge wveform in Fig is pplied to 1-mH inductor, find the inductor current i(t). Assume i(). v(t) 5 5 Figure 6.68 For Pro Find v, i, nd the energy stored in the cpcitor nd inductor in the circuit of Fig under dc conditions. t i(a) 1 Figure 6.66 For Pro t (ms) Ω v F i 3 A Ω.5 H Figure 6.69 For Pro Ω

6 6.7 For the circuit in Fig. 6.7, clculte the vlue of R tht will mke the energy stored in the cpcitor the sme s tht stored in the inductor under dc conditions. R 6.5 Using Fig. 6.7, design prolem to help other students etter understnd how inductors ehve when connected in series nd when connected in prllel. 16 F 5 A Ω mh 3 Figure 6.7 For Pro eq Under stedy-stte dc conditions, find i nd v in the circuit in Fig Figure 6.7 For Pro i mh 5 ma 3 kω v 6 F kω 6.53 Find eq t the terminls of the circuit in Fig Figure 6.71 For Pro Section 6.5 Series nd Prllel Inductors 6.9 Find the equivlent inductnce of the circuit in Fig Assume ll inductors re 1 mh. 6 mh 8 mh 5 mh 1 mh 8 mh 6 mh mh Figure 6.75 For Pro mh 8 mh Figure 6.7 For Pro An energy-storge network consists of seriesconnected 16-mH nd 1-mH inductors in prllel with series-connected -mh nd 36-mH inductors. lculte the equivlent inductnce Determine eq t terminls - of the circuit in Fig mh 6.5 Find the equivlent inductnce looking into the terminls of the circuit in Fig H 9 H 6 mh 1 H 3 H 5 mh mh H 6 H Figure 6.73 For Pro mh Figure 6.76 For Pro. 6.5.

7 6.55 Find eq in ech of the circuits in Fig The current wveform in Fig. 6.8 flows through 3-H inductor. Sketch the voltge cross the inductor over the intervl 6 t 6 6 s. i(t) eq () Figure 6.8 For Pro t eq 6.59 () For two inductors in series s in Fig. 6.81(), show tht the voltge division principle is Figure 6.77 For Pro () 6.56 Find eq in the circuit of Fig v v s, v 1 v s ssuming tht the initil conditions re zero. () For two inductors in prllel s in Fig. 6.81(), show tht the current-division principle is i 1 1, i 1 1 ssuming tht the initil conditions re zero. 1 v 1 v s v i 1 i 1 Figure 6.78 For Pro eq () Figure 6.81 For Pro () *6.57 Determine eq tht my e used to represent the inductive network of Fig t the terminls. 6.6 In the circuit of Fig. 6.8, i o () A. Determine i o (t) nd v o (t) for t 7. eq i H 3 H di dt 5 H e t A 3 H 5 H i o (t) v o Figure 6.79 For Pro Figure 6.8 For Pro. 6.6.

8 6.61 onsider the circuit in Fig Find: () eq, i 1 (t), nd i if 3e t (t) ma, () v o (t), (c) energy stored in the -mh inductor t t 1 s. v o i 1 mh i mh 6.6 The switch in Fig hs een in position A for long time. At t, the switch moves from position A to B. The switch is mke-efore-rek type so tht there is no interruption in the inductor current. Find: () i(t) for t 7, () v just fter the switch hs een moved to position B, (c) v(t) long fter the switch is in position B. 6 mh Ω B i t = A Figure 6.83 For Pro eq 1 V.5 H v 5 Ω 6 A 6.6 onsider the circuit in Fig Given tht v(t) 1e 3t mv for t 7 nd i 1 () 1 ma, find: () i (), () i 1 (t) nd i (t). Figure 6.86 For Pro v(t) 5 mh i 1 (t) mh i (t) 6 mh 6.65 The inductors in Fig re initilly chrged nd re connected to the lck ox t t. If i 1 () A, i nd v(t) 5e t () A, mv, t, find: () the energy initilly stored in ech inductor, () the totl energy delivered to the lck ox from t to t, (c) i 1 (t) nd i (t), t, (d) i(t), t. Figure 6.8 For Pro i(t) Blck ox v t = i 1 i 5 H H 6.63 In the circuit of Fig. 6.85, sketch v o. Figure 6.87 For Pro i 1 (t) v o H i (t) i 1 (t) (A) 3 i (t) (A) 6.66 The current i(t) through -mh inductor is equl, in mgnitude, to the voltge cross it for ll vlues of time. If i() A, find i(t). Section 6.6 Applictions 3 6 t (s) Figure 6.85 For Pro t (s) 6.67 An op mp integrtor hs R 5 k nd. mf. If the input voltge is v i 1 sin 5t mv, otin the output voltge.