sample problems 01

8/3/2019 Sample Problems 01

1/19

r (sigma) is the eleclrical conductivity. Ifa = 5.8 x 107 U/n for copper: (a) wha!lensrh (in feer) of # 18 copper wire (diameler : L024 mm) has a resistance of I O?(,) If a circuit board has a copper'fojl conducrin8 ribbon 0.0013 in thick and 0.02in wide thatcan carry3 A safely a160"C, what powerdoes this current deliver to aconductor 6 in lonsl4 ln the circuit of Fis. 2-27. 6nd le a.d G if the 5 A sou.ce is supplyins 125 w.

ilry.rlm.lt.l L.w..nd slmpl. Clrcqlrr 49

2-271 See Prcb. 4.

2.2a: Se Prob. 5

5 UseOh 'stawand Kirchhoff's laws on rhe circuit ofFis.2-28 tofind: (a) ui,! (r)the power provided by the dependent sourcei (.) v".

6 (a) Use Ohm's and Kirchhoff s laws in a step-by,stp procedure to determine allthe voltages and currents itr the circuit of Fis. 2,29. (,) Compute the powerab\orbed b) e\eq elemenr and \how rhat rhe,um F rero.

7 h the circuit shown in Fig. 2,10, find the power absorbed by the: (a) 4-A source;(r) 2-O resislori (.) 12-O resisror; (d) 6-() resistor; (e) vokase source %.2.29! Se

2A 2-25 S7

+ a3 illrl


2/19

tg En lr..rlng Clrcdt An.lyrlr

Fie. 2.31: See Prob. 9.2-32. (bl Lcr rr now extend across :\-- -n ihe lefi, and asain find l.

8 A certain circuit contains six elements and four nodes. numbered 1- :. l. 6r..Each circuit element is connected between a differeht pair ofnodes. T::::direcled from.ode I to node lin that branch is irz : 15 A, rvhile i! = ! :, -r, t,r, and L, if ?,r = | (a) 0i (r) l8 Ar (.) lE A.9 Find the power being absorbed by elemenl X in Fig. 2-31 if i!isa: j -l-lresistori(b) 2'V independent voltage sou.ce, + reference on leili(cri=aEvoltage source, - .eference on left,labeled l9iri (d) 52-mA independeE:].:source, arrow direcled ro rishr.20rl 30f,l

l0 (d) Find iin the circuil show. in Fig.4 {} aod 50 V elemenls. + refere.ce

Frg. 2.35: See Prob 1

Fiq.2.35: See Prob

500v

F19.2.32: See Pob. 10.1l Forthe batlery charsermodeled by Fis.2-31:(a) findR so tha! a charsin8 cL::--of 2.5 A flows: (r) fird rR so thar 25 W is delivered to the 11-V ideal roj:lEsource; (.) find R so lhat 25 W is deliveied to the combinarjon of0.04 O and: i

f-------l0.05 [}

L_________iBntry .harge.Fig. 2.33! See Prob. 11.

0.04 rltt v

L___-____J

0.2 n

0.6 a30v

Flg.2-34r See Probs. 1212 In the circuii show. i. Fig. 2-34. X is a simple circuit etemenr. Assume that -f sabso.bio8 100 W and: (a) find R ifx is a resistor Feater rhan 5 O: (r) find 1.. -re,erence ar rop. ii X i\ dn lndependent vohdse \ource. r r \ .

15o> :50sl

Fis.2.37! See Prob.


3/19

t0 i)

2.35r See Prob- 141's Find the power absorbed bv each element in the circuit illustrated in Fig

o.2ia

I 6 S),20A 4Q

16 In Fis. 2-37, find the power supplid bv each of the sources if thesouce is labeled: (a) 3ir i (r) 3!,i;;;p;;;l;;,b";;; eac"h circuit erement in the singre'node'pair circuit or 'Flg. 2{ar Ses Prob. 17'

26l See Prob. 15.

17

2.37! See Prob. 16.


4/19

l8 In the chcuii of Fig. 2-39, X is a simple circuit lenrt. Assume that x is absort!ing 100 W and: (a) find R ifx is a resistor larger than 50 Oi (r) find L, referenc.arrow dircted down, ifx is an independent cunent source, i, > 2 A.

See Probs. 1819.

2.4O! See P.ob. 20.

l9

100sl

Let the downward cudent throuSh the l0G0 resistor i6 Fig. 2-39 be 1.2 A.Assum that x represents an unknown circuit element. (a) Find the absorbdpower for each element in the circuit. (r) lrx is a resistor, sive ils resistance R(which migh. be nesalive): ifir is an independent cuneni source, give i,, includinsreference direction; and if it is an indepndnl voltage source, give u", inciudi.SDolarity. (c) Repeat parts a and /, if the 1.2-A currnt is direcled upward.(a) Apply the techniques used in sinple rcde-pair analysis to the upper right node

30!l

Ftg. 2.42: See Prcb. 2i20

5Q

2.zlt! See Prob. 21.

zoQ R",!-

Fig. 2.43! See Prob.

Fla. 2.rlll: See Prob

10l)

o.5i 30sl


5/19

:' *]ErD.rln.nrd L.x. tnd 3lhDl. Clrcult 5ilin Fis. 240 and find i,. (b) Now work liilh lhe upPer letl node and find u.. (.,How much power is the IGA source Seoeratins?2l Find R.4 for each of lhe three rsistive networks shown in Fig. 2_41.22 For rhe network of Fis. 2-42: (a) find A.q ifR = 14 O; (r) find R if R.4 : 14 O.

lsl R l.to

4.5 f,

9rl

Flg. 2.a+ S Prob. 24.

2A 5Q2J Find R,a lo, each nerwork shosn in fi8. 2-4:t

2A 25 {1,15 Q i"c*

t R iR

R=50O(')By combinins sources and rsistances

t.l A

in the circuit of Fig. 2-44, find u. and i, .

212r see Ptob. 22-

(b)

i

14

P ?a1,.,.44 (

6f}10rl o

A(ir52.4o


6/19

5a hlE .lnl Elrcult ln.lyrl.

Flg. 2.45: See Prob. 25-

25 Use source and resislance combinations to simplify the circuit of Fig. 2-45 aD.then find i, and .)1.7{7

ilt20v

26

21

Given 10 resistors, each having a resistance of 20 O: (a) what is the smallesr(nonzero) equivaleni resistarce that they could be assembled ro produce? (r)What is the largest (finit) equivalem resistance? Show lrow some ofthese resis-tors misht be combined to produce ad equivalent resislance of: (c) 29 Ot (d) 6 O.Fjnd the equivalent conductance for each ofthe nelworks of Fis. 2-46.

Fig. 2'4at See Prob 29

Fig. 2.49: See Prob' 3

Fts, 2.!iO: Se P'c!

50 mu l0 m?J

k)Flg. 2.46! Soe Prob. 27

10 m?t


7/19


8/19

I brha..tE Clrcult Anrl,.lt33 (a) Use voltase division, cuBent division,.od resistance combinationb nnd i,lhecircunolFrB. 2-52. rr) Iouh"t value\houtdrhe l-O r(,i,r"nc..bechangd

lo10sl

IQlZy

69 liylr2A

Fig.2.5& See prob 34.3,1 The circuil shown in Fig. 2 5l shos,s seve.at cxamples of independent curetrand voltase sources in series and parallel. (d) Find the power rbsorbed by ea.nsource. (,) To whai value should the 4-V source be changed to.educe rhe pow-supplied by ihe 5-A source ro zero:,l5 A cerlain op'amp has a gain,4 ol:0 000 lnd a.esinaoce, R, :50 kO, i.side lb.op-amp between the invertiDg a.d noninverring inpur!. The op,amp is cooneclsias a voltase follorver lvith r. = I v. Find: (.r.,,i (r) o,i (.J the power iupplied bl36 {a) Find !, for the volrage lbllowe. shown in Fts. 2-54a if A is larse. (r) Theneawork shown in Fig. 2-j4, is connected to the fottower ourput. Find u,.

\bj37 (d) Find u. for rhe ci.cuir shown in Fig_ 2,55 if,,{ is large. lr) ff the op-amp isremoved from the circuit and poinrs a and , are conrected loserher. what is r,?

rle. 2.52: See Prob. 33-

Fl!. 2.5t[ See Prob. 36.

Fla. 2.55! See Prob. 37.

3-1lntroduction

tov

10 kr,

l0ko lkQ


9/19

s:. ;.r, t(){ Ell.tr..rlng Cltcdt ln.lY.i.

1

2 Use nodal analysis to 6nd up in the circuit shown in Fig. 3-44.

204Fig. 3./t4! See P.ob. 2.

13 Ure nodal aEalysis on the circuil siven in Fisbeing supplied by the 5-A source.too v

I 45 1o find: (a) uri (r) thc power

I 47, and then find the

:

Fig. 3-45: See Prob. 3.Make use ofnodalanalysis to fild ,, and the power delivered to the 50_O resistorin the cjrcuit of Fig. 3 46.

Fig. 3.tlG Se Prob. 4. Flg. 3.4?: See Prob. 5-Ser up nodal equations for the circuir illus!.ated in Fig.power tupplied by tbe 5 V source.Usc nodal analysis to fiod u, in the circuil of Fig- 3 48.

4

.6ov ll

2?ta


10/19

2!7

Ftg. 3.4a: See Probs. 6,12 and 28.

-----\j;_ 20v6A 30s}

Dno 3", ( D,o 15 ll en rn(8 In Fig. 3-50, 6nd u, throud the use of nodal analysis.

In the cncuitofFis.3'5,, use meshanalysis to:(a) find the power deliverd to the4-O resistor. (6) To what voltase should the 10GV battery be changed so ihat nopower is delivered 1o ihe 4:O resistor?2A lOoV

+----- ... . ,l'-

7 Analyze lhe cinrurr ol tis. J-49 u\in8 node \olrdge\ dnd find lhe poqe! being' supplied by the eA source.

Fie. 3.49: See Prob. 7.

Flg. 3.5O: Se Prob. 8-

Fis.3-51! Se Prob.9.

:'

l

/9

dn'_. .- _L

0.06?t + 0.03u10v


11/19

Erdna.rha Cltcult rn.ayrlrl0 Use nesh analysis on the circuit shown ir Fig. 3-52 to find the power aupplied by

41 In Fis. 3-53, every resistance is 6 O and every battery voltaee is 12 V. Find i,.

{i^Flg. +53: Sse Prob. 11i!. 3.52: See Prob. 10.

Flg, +5a! See Prob. 13.

F19.3.55! See Prob. 15.

12

n4tt4

In the circuit of Fig. 3-48, change the right-hand element to an 8-A independertcurrent source, arrow directed upward, and use mesh analysis to find the powerab'orbed by Ihe l-O rcsisror.Use 4esh analysis on the circuii of Fig. 3-54 io 6nd the values.of all the meshIn the circuit of Fis. 3-4r, use mesh aoalysis to find i,, the cuIrenl flowidsdownward h R, if,, : 1.234 321 Y-

1f, to

2oo o 600 o

x,

i, Rr


12/19

!orn. U..ftrt t.cn qu.. ot Ctrcun ln.tr.I. iO,a 15 ln the circuir shown in Fig. l-55: {ar if rr - 20 V and u, = 0. ir - Lj A: 6nd /.r ifu. = 50VaDd u, = 0;(r) iful = 20 v and,, :50 V, il= 2 A, while i. = -t A if ,,r = 50V and rj = 20V; fiod r.if ur = 30Vand u, = tooV16 Use super?osition wilh the circuir of Fis. 3-56 ro find !.5!l to'l

t7 With refrcdce to the circrit outtined in Fis. 3-57, when u" = t20 V. it is found thati, - I A, u, - 50 V. and the po$er delilered ro R, is 60 w. tfcon Ed reduces u. ro105 V. frnd new talue\ for i . ur. and rhe power dehlered ro Ar.

Flg. 3.3'6! Sse Prob. 16_

Fle. 3.57: See Prob. 17l8 Use ihe superposition theorem on the circuit shown in Fig. t_jE to find i.

Flg; 3.58r See prob. 19.

160V


13/19

ioa Cnshcilns Clrcuia An.lyil.

Fit. 3-59! See Probs. 19and 29.

Fig. 3.AO: See Prob. 20.

Fig. 3.6'l: See Prob. 22.

Fig.3.e2: See Prob. 23

49 The circuit illust.ated in Fig. 3-59 contains a dependent source. Us the superpo_sition theorem to lind the current 1.

20 In the circuit of Fig. 3'60, use superposilion to help find the powr.absorbed bythe: (a) 6-V source; (r) I A source: kJ l2-V sourcei (d) 2-A source.

2t

22

A Radio Shack type 222 flashliSht bulb is intended for use with two 1.55_Vpeolight (AA) batteries in series. Thebulb, howver, is marked "2.25 V,0.25 A."Assuming all markinSs a.e corect, what praclical voltage source miSht be used tomodel one of the batteries?By making repeated soulce iransformations ard resistance combinations for eachnetwork in Fig. 3-61, replace the network ao the left of terminals a-, with theseries combinarion of a single independent voltage source aod a single resistor-

(at23 In the circuit of Fis. 3-62, what value of Rz : (a) will absorb a maximum powerfrom tbis netwo.k and what ispr m.x? (,) will have the naximum voltage across itand what is u.,.*1(.) will have a maximumcurrent throush it and what is rr..,*?

lb)

20sl


14/19

Some U.Glul Te.hnique. ol Circult ^rdr.l. 'llr924 Consider the practical voltage source to the left ofrerminals a,, in Eic. 3-63. (a)What must be the value of rR. to cause the maximum possible pqrd to b drawnftor.l the pta.ti.al sourc? I (r) Whar is the value ofthis max;mom power?

10v8St

2sl

24'140f,} 60f,l

FiE. 3.63: See Prob. 24.

Hg. 3-q! See Prob. 25.

Fig. 3.6+ Se Probs. 26and 30.

10 terminals a-, for ihe circDitind the ThEvenin equivaient cAcuit wiih respeclshown in FiE. l-65.20 s, 40r,

50v

)rza\7

12f,}

It4a (

25 (a) U se rhree separaie analyses to find u,," , i,. , and i,, with respect to termiDalsa-, for the circuit shown in Fis. 3-64. (b) Draw the Thvenin a.d Noron equiva-lenis as seen a! d-,.5Sl

15 Q

26

27 (z) Delermine rhe Thvenin and Norton equivalent circuits as seen ar rerminalsd-, for the nerwork of Fig. l-66. (b) Rerlace the 5-A source wiih a dependenlvollage source labeled 5i, (+ reference at rhe righo and again find the Th6ve.iaa.d Norto! equivalents-

Fis, 3.66: Se

b') ro;,


15/19

tto Ei{hr..rlnt Clrcult An.lr.l.28;in the circuit of Fis. l-48, frnd the Thevenin equivalenr of the network (d) to thelft of the 8'v source: (,) to rhe riSht of the 6V source'29 (a) Refer to the cncuit shown in Fis 3'59 and find the Thevenin equivalent circuitfaced bv the 3-oresistor- (r) Find I. (c) Chanse the 3"oresisrorro 13 o and againfind ''0 Ifthe vollage u. acrossorthe current i. = u./R.lhrough a general load reJstanceR. is known, then the Thevenin or Nodoo equ;lalenl mav b determined easilv

since u,, = limi/-. uz a6d 1,. : limr.-o iz. (a) Find u. (+ sisn , erminal z")for the circuil of Fig. 3_65 if a.esisrance Rr is conrccted btween d and ''r) Use The exPressions above 1() determine uo, and ir.3l Fild the Thevnin equivalent circuit for thq network shown in Fis 3 67'

200 I} too o Fla.3.?t: See

Flg. 3-72: See

Flt. 3.?3: See

Flg. .3.7/r: See

Flg, 3.67! See Prob.31.

Flt. 3.64r See Prob- 32.

Flg. 3.69: Se Prob. 34-

v12 Delermine the Theverin equivalent circuit of.he network shown in Fis. 3-68.

33

34

20\'

15 For the circun shown in Fi8. 3'70, coflstruct a lree in which ur and .,: are tiee'b.anch voltases, write nodal equalions. and solve ior ur.

The voltaee follower shou,n in Fi8. 3-28 is modified by inserting a finite Ai =l0 kO betwen the terminals across which .,, is defined. Find the oew Thveninequtralenl.(a) Construcl all possible trees for.he linear sraph shown in Fi8. 3-69. (,) Iftheloptwo branches are voitage sources ard the left branch is a cunnt source, sbow

tIt

I1IJII

80vFl!. 3.7Or See P.ob. 35.


16/19

&m. U..lu! t chntqu.. al C{rcuh lnrtt.l. ill36 Construct a suitable tree for the circuit of Fig. 3-71 . assign tree-branch voltages,write KCL and conirol equations, and find i:.

a.Dd again

Flg.3.7!: Se Prob. 36-toiz

of Fig. l-74 and w.ite the singl

37 Us nodal analysis with tree-bmnch voltaaes on the circuit oI Fig. 3-72 to derer-mine what value of v: will cause u. = 0.

38 For the circuit shown in Fig. 3-73, construct a iree in which ir and 4 are linkcunents, write loop equationst and evaluate ir and ,r.

5sl 2A10 f,, 20 f,t.a 50f,l 20v (19 (d) Construct a suitable tree for the circuitquation oecessary 10 find ir. (6) Find ir.

30v

Fig. 3.72: See Prob. 37.

Flg. 3.73: See Prob. 34.

FIt. 3.7a: Se Prob. 39.


17/19

It2 lliiln cdr! Crrcutr fu.tyrtr

0.8 f,l

40 Devise a lree for lhe circui. shown in Fig. 3-75 for which aI loop curren.s flowlhrouSh rhe l-O resi\tor. Find i.

Fig. 3.75: See Prob. 40.

Fle. 3.7G: See Prob.41.

Fig, 3.?7: See prob_ 42.

42 Figure 3-77 shows one form of rhe equivalenr circuit for a rransistor amplifier.Determine the opeilcircui! value of u? and tle outpua resislarce (R/r) of rheamplifier-

41 Use seneral loop analysis on the nonplanar circuit of Fis. 3-76 ro find ,,.

2ko


18/19

rndix 5Answers to Odd-Numbered Problems Chaole':

I b\ l34z milht (b\ 196.1kJ; (c) 22.7 days; (d) Lois Lane3 (a) 6.97 horsesi (b) 0.543liter515C7 (a) -35.6 mci (b) -34.0 mA; (c) 13 4l pC9 (a) 4.38 W; (r) 0.400 J11 (a) 0; (r) 013 -32 W, -16 W,24 W,56 W, -32 W

chaptor 1

Chapler 2

I),II1517

t (a) |.661 {l; (b) 0.144 o; (c) 640 w3 (a) 156.7 ft; (r) 1.410 Ws (a) -26v;(b) 320 W; (c) 6 v7 (a) -96 w; (b) 32 wi (c) 21.3 w; (d) 16.67 wi (e) 10 w9 (d) 51.1 Inw; (r) 52.2 mw; (c) -51.5 mw; (d) -51.0 mWIt (a) 1.110 O; (r) 1.230 O; (c) 1.241 O13 (o) pn = -@ W, po, = 80 W, p- : 280 W, po6 = 240 W;(r) 0.? O, t4 v (+ at top),20 A (down); (c-a) 600 w, 80 w, -920 $.240 W; (c-b) -2.3 O, 46 V (+ al lop), 20 A (up)po: = -148.8 W, pm = -1090.9 W, pr = 743.8 W. po: 495.9 Wps= 10.45mw,ri- 45.7 mW,p7 = 4l.8mw,p r: -27.4mW.Pa=209mW19 (a) pzs = 576 W, p5 = 600 W, p, = - 120 W, pr00 : l44 Wt(b). -120 fi, I A (up), 120 V (+ at top); (c-a) 576 W, 600 W, -144 Wt (c-b) - 10.91 O, l1 A (down), 120 V (+ at bottom)2l (a\ 25 At (b\ 20.3 Or (c) 22.5 O23 (a) 22.3 ai @) 21.8 At k) 22.1 A25 5 A.-+',7.5 V21 (a) t1.'78 'J'].A: (b) 4.32lJ29 (a\ 2.29 ,ltA, (b) 2.67 A3l (a) 300 V; (r) 120 v; (.) 0.333 A

33 (a) 1.481 A; (D) s.39C}


19/19

Anrv.rt to Ortd.iaunbarod P'.obLri. 62-50.0 &V; (r) 0.999 950 nw537 (d) 0.999 950 V; (r)(d) 2 v: (r) 0.5 V

I (d) -4.83; (b) 2003 (a) -60.9 Vi (r) 195.7 w5 25.6 W7 12. t3 W9 (a) 2580 W; (b) -32 vl1 I AIl t.2 A.4.2 A,2 A,3.2 At5 (a) 3.75 Ai O) 4.43 Al7 2.625 A,43.75 V. 15.9 W194A2t 1.55 V. 1.7 r)23 la) 12 {1,0.7,i W; {r) r. 6 Vt kJ 0, 0.5 A25 ld) -22.5 V. -2.4 A. 9.375 O; (b) -22.5 V, 9.375 O; -2.4 A,9.315 A27 h) 32 v. 4 A;8 A, 4 {): (b) 48.6 V. 3.24 Oi 15 A, 1.24 O29 (.r) 20 V, -8 O: (r) 4 A; (.) -4 AIt t38 033 4.999 500 V, 0.199 976 ll35 19.02 V3'7 1vl9 (d) 8ir + 6(,, - 2l :0 4lr + 30 = 0; (r) 0.2 A4t 1.8t8 A

i!It

I (a) I.618 v: (r) 0.0711 V,0.549 s3 (a) 18 A; (b) 160 J; (c) 320 w5 (a) -1 + 0.5 cos 500r + 0.4 sin 500/ A; (r) 0.1613 J'7 (a) 90 pI, lb) 94.2 tts9 {a) 10.009e ro * o.ool v (r) loe ,o,v1L la) 0.0677 Jt (b) 0; (.) -8.83 V13 (a) 6.43 H; (b) 2.83 H15 5 in series in parallel with 2 in seriest7 (a) 9.66 r. (b) '7.t21, k\ 11.24 t19 (d) l0 rur + 2 x l0 6(Di - vr: i",2 x l0-6(ui - ui) +2tfil; urdt + 3 = O (+ur top lefr, +u? top right);(r) 1000(,, - i") + 5 x tosll iLdt + 8+0.005ii=021 (d) See sketch below:.O.2(uc - 2e-tu) + O.lua- - 0.M(2e-r0, - uc)0.05up :0, -0.05u,1 - 0.1e-r0, + 100_[j (-u* + vc - 2e-tot\dt = 0:(r) see sketch below; 5i, + I0l&l + 0.2i, + r, +o.le lurdt - 2e tot = O,O.OliL + 2O(i. + 0.1"-r0r) +

l0li/1.2i, + iL + o.|e-totldt - 2e til = 0

sample problems 01

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