196 Circuit Analysis with PSpice: A Simplified Approach
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1 196 Circuit Anlysis with PSpice: A Simplified Approch i, A v L t, min i SRC 5 μf v C FIGURE P7.3 () the energy stored in the inductor, nd (c) the instntneous power input to the inductor. (Dul of Prolem P7.). t t Ans. () l( t) = mw-t, 0 t 60s; l( t) =-, mw-t 1 t 60 t 0 s; l ()= t 0, t³ 0 s. () w()= t qv= mj, 70 1 æ t 0t ö 0 t 60s; wt ()= ç mj, 60 t 0 s; 180 è 36 3 ø t wt ()= 0, t³ 0 s. (c) pt ()= mw, 0 t 60 s; æ t 0 ö pt ()= ç - mw, 60 t 0s; p()= t 0, t³ 0 s. 180 è 18 3 ø P7.33 The voltge wveform in Figure P7.33 is pplied to n initilly unchrged 0.5 μh inductor. () Derive expressions for the inductor current during the time intervls: 0 t m s, t 0ms, 0 t 60 ms, 60 t 80 ms, nd t > 80 ms. () Wht is the flux linkge in the inductor t t = ms nd t t = 50 ms? Check the finl vlue of current ginst the finl flux linkge. (c) Wht is the energy stored in the inductor t t = 80 ms? (d) How do the expressions for the current through the inductor derived in () ove chnge if the inductor current ws initilly 0.5 A? (Dul of Prolem P7.17). Ans. () i()= t. t ma, 0 t m s; it ()=- t 50t- 50 ma, t 0 m s; it ()=- 30t 1350 ma, 0 t 60 m s; it ()= 0. 75t - 10t 050 ma, 60 t 80 m s, v(t) = 750 ma, t 80 μs. () 75 nw-t t t = μs, nd 75 nw-t t t = μs; (c) 0.1 μj; (d) ll currents re incresed y 0.5 A. FIGURE P7.3 P7.3 Given i SRC (t) = 0.1t A, t 0 s, in Figure P7.3, with no energy stored in the circuit for t 0. Determine t t which v L = v C. Ans. 0.1 ms. P7.35 Given i SRC (t) shown in Figure P7.35, with zero initil energy storge for t 0. () Express v L nd v C s functions of time nd sketch this vrition. () Determine (i) the instntneous power sored y L nd C s function of time, nd (ii) the energy stored y L nd C t t = s. Ans. () v L (t) = mv, 0 < t < 1 s, nd v L (t) = 0, t > 1 s; v C (t) = t kv, 0 t 1 s, nd v C (t) = (t 1) kv, t 1 s. () (i) p L (t) = t mw, 0 < t < 1 s, nd p L (t) = 0, t > 1 s; p C (t) = t 3 kw, 0 t 1 s; p C (t) = t kw, t 1 s; (ii).5 kj. P7.36 Determine V X in Figure P7.36, ssuming dc stedy stte. Ans. 1.6 V. P7.37 Determine in Figure P7.37, ssuming dc stedy stte. Ans. 1 A. P7.38 Determine in Figure P7.38, ssuming dc stedy stte, ll resistnces re in ohms, ll inductnces re 1 H, nd ll cpcitnces re 1 F. Ans. 75/1 = 5.36 A. P7.39 Determine the energy stored in the inductor in Figure P7.39, ssuming dc stedy stte. Ans. 0.5 J. i SRC v L 1 mf v C i SRC, A t, s v, mv FIGURE P t, μs V 1 H 0 1 μf V X FIGURE P7.33 FIGURE P7.36
2 Cpcitors, Inductors, nd Dulity A 1 μf 1 V 60 C 0. H 5 μh 1 μh 5 μf FIGURE P7.1 FIGURE P7.37 C L R R R L C A FIGURE P7. 0 V 1 50 V P7. Derive the reltion etween R, L, nd C in Figure P7. so tht the sme energy is stored in L nd in C under dc conditions. Ans. L = CR. FIGURE P7.38 Series nd Prllel Connections of Cpcitors nd Inductors FIGURE P V 1 μf H P7.3 () Determine the equivlent cpcitnce etween terminls in Figure P7.3 if ll the cpcitnces re 1 F. () Determine the equivlent inductnce etween terminls, ssuming tht ll cpcitors in Figure P7.3 re replced y inductors of 1 H. Ans. () /3 F; () 3/ H. P7. () Determine the equivlent cpcitnce etween terminls in Figure P7. if ll the cpcitnces re 1F. () Determine the equivlent inductnce etween terminls, ssuming tht ll cpcitors in Figure P7. re replced y inductors of 1 H. 0.5 V 1 F F 1 H 0 H Ans. () = 037. F; () 1 =. 73 H. 1 P7.5 () Determine the equivlent inductnce etween terminls in Figure P7.5 if ll the inductnces re 1 H. () Determine the equivlent cpcitnce etween FIGURE P7.0 P7.0 Determine the energy stored in the circuit in Figure P7.0 in the dc stte, ssuming ll resistnces re 5 Ω. Ans. 0.5 J. P7.1 Determine C in Figure P7.1 so tht the sme energy is stored in C s in the inductor under dc conditions. Ans. 0.5 mf. FIGURE P7.3
3 198 Circuit Anlysis with PSpice: A Simplified Approch FIGURE P7. FIGURE P7.7 FIGURE P7.5 terminls, ssuming tht ll inductors in Figure P7.5 re replced y cpcitors of 1 F. Ans. () 1/5 H; () 5 F. P7.6 () Determine the equivlent inductnce etween terminls in Figure P7.6. () Determine the equivlent cpcitnce etween terminls, ssuming tht ll inductors in Figure P7.6 re replced y cpcitors of the sme vlue in mf. Ans. () 18 mh; () 850/7 = 11. mf. P7.7 () Determine the equivlent inductnce etween terminls in Figure P7.7, ssuming ll inductnces re μh () Determine the equivlent cpcitnce etween terminls, ssuming tht ll inductors in Figure P7.7 re replced y cpcitors of the sme vlue in μf. Ans. () 3/ μh; () 16/3 μf. P7.8 Repet Exercise 7. replcing cpcitnces y inductnces of 0.5 H (Figure P7.8). Ans. 0.8 H. P7.9 Repet Exercise 7.11 replcing inductnces y cpcitnces of equl vlue in frds (Figure P7.9). Ans. 0/131 = 0.31 F. P7.50 Ten 1 μf cpcitors re chrged in prllel to 00 V. Determine () C eqp nd () the energy stored in the equivlent prllel cpcitor. (c) Verify tht the energy mh 80 mh 0 mh 60 mh FIGURE P7.8 FIGURE P7.9 1 F F F 0. F 1.5 F stored in this cpcitor is the sum of the energies stored in the individul cpcitors. After the cpcitors re fully chrged, they re connected in series. Determine (d) the voltge cross the equivlent series cpcitor nd (e) the energy stored in this cpcitor. (f) Deduce C eqs for the chrged cpcitors. Is it the sme s tht for initilly unchrged cpcitors? Ans. () μf; () 5 J; (c) 0.5 J is stored per cpcitor; (d),000 V; (e) 5 J, (f) 0.1 μf, yes. P7.51 All inductors in Figure P7.51 hve n inductnce L nd ll cpcitors hve cpcitnce C. Determine L eq in series with C eq tht re equivlent to the comintion of L nd C shown etween terminls nd. Ans. L eq = 11 L/6, C eq = 3C/7. 1 F 10 mh FIGURE P7.6 FIGURE P7.51
4 Cpcitors, Inductors, nd Dulity 199 Dulity P7.5 Given the circuit of Figure P7.5, () derive the dul circuit, () compre the resistnce or conductnce seen y the independent source in ech circuit, nd (c) compre the power delivered or sored y ech circuit Ans. () 18 A source in prllel with 9, 1, nd S; () 36 Ω, 36 S; (c) sources deliver 9 W, 9 Ω/9 S resistors dissipte.5 W, 1 Ω/1 S resistors dissipte 3 W, nd Ω/ S resistors dissipte 3.75 W. P7.53 Given the circuit of Figure P7.53, () derive the dul circuit, () compre the resistnce or conductnce seen y the independent source in ech circuit, nd (c) compre the power delivered or sored y ech circuit Ans. () 1 A source in prllel with S nd with series comintion of 6 nd 1; () 6 Ω, 6 S; (c) sources deliver W, the Ω/ S resistors dissipte 8 W, the 6 Ω/6 S resistors dissipte 3/3 W, nd the 1 Ω/1 S resistors dissipte 16/3 W. P7.5 Given the circuit of Figure P7.5, () derive the dul circuit, () compre the resistnce or conductnce seen y the independent source in ech circuit, nd (c) compre the power delivered or sored y ech circuit Ans.() 30 A source in prllel with S, 0 S nd series comintion of S nd CCVS; () 60 Ω, 60 S; (c) independent sources deliver W, Ω/ S resistors on the LHS dissipte.5 W, 0 Ω/0 S resistors dissipte 5 W, Ω/ S resistors on the RHS dissipte.5 W, dependent sources deliver W. FIGURE P7.5 FIGURE P V 1 V FIGURE P A 5 P7.55 Given the circuit of Figure P7.55, () derive the dul circuit, () compre the resistnce or conductnce seen y the independent source in ech circuit, nd (c) compre the power delivered or sored y ech circuit Ans. () 3 V source in series with prllel comintion of 5 nd S nd prllel comintion of S nd VCVS; () 5 Ω, 5 S; (c) independent sources deliver 5 W, 5 Ω/5 S resistors dissipte 5 W, Ω/ S resistors dissipte W, Ω/ S resistors in prllel with dependent source dissipte 16 W, dependent sources sor 1 W. P7.56 () Derive the dul of the circuit of Figure P7.56; () represent the two circuits in the dc stedy stte; (c) compre voltge division in the given circuit with current division in the dul circuit; (d) compre the power delivered or sored y ech circuit Ans. Current source in prllel with S, μf, nd series connection of 0 S nd μh; () V source pplied to Ω in series with 0 Ω, A source pplied to S in prllel with 0 S; (c) V divides in proportion to resistnces, A divides in proportion to conductnces; (d) sources deliver 7.5 W, Ω/ S resistors dissipte.5 W, 0 Ω/0 S resistors dissipte 5 W. P7.57 () Derive the dul of the circuit of Figure P7.57; () compre R in of the dul circuit with R in in Figure P7.57. Ans. () R in in Figure P7.57 is Ω, R in of dul circuit is 0.1 Ω. P7.58 () Derive the mesh-current equtions using the mesh currents shown in Figure P7.58, () deduce the nodevoltge equtions of the dul circuit, nd (c) derive the circuit tht will give these node-voltge equtions with respect to specified reference node. Ans. Y-connection of 1,, nd 3 mf inscried in Δ-connection of 1,, nd 3 A current sources. P7.59 Verify tht the mesh-current equtions of the circuit of Figure 7.38 re the dul reltions of the node-voltge equtions of Figure μh 30 V V X 0.1V X V μf 0 FIGURE P7.5 FIGURE P7.56
5 00 Circuit Anlysis with PSpice: A Simplified Approch R in V X I Y V X 5 I Y 3 mh i 3 V 1 V i 1 3 V i mh FIGURE P7.57 FIGURE P7.58
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