d i t e e dt units of time are s. Determine the total charge that has entered a circuit element for t 0. Answer:

Transcription

1 Chaper Homework P.2-, 3, 4 P.3-2, 4 P.5-, 3, 5, 6, 7, 8 P.2. The oal charge ha has enered a circui elemen is q() =.25( e 5 ) when and q() = when <. Deermine he curren in his circui elemen for. Answer: i() = 6.25e 5 A d i e e d 5 5 =.25 = 6.25 A ( ) ( ) P.2-3 The curren in a circui elemen is i() = 4 sin 3 A when and i() = when <. Deermine he oal charge ha has enered a circui elemen for. Hin: τ q() = i( τ) dτ = d τ = q( ) = i( τ) dτ + q( ) = 4sin 5 d cos 3 cos 3 C τ τ + = τ = < 2 2 2< < 4 P.2-4 The curren in a circui elemen is i () = where he unis of curren are A and he 4 < < 8 8< unis of ime are s. Deermine he oal charge ha has enered a circui elemen for. Answer: < < < 4 q ( ) = where he unis of charge are C. 8 4 < < 8 8< ( ) ( ) C for 2 so q(2) =. q = i d = d = ( ) ( ) ( 2) C for 2 4. In paricular, q(4) = 4 C. q = i d + q = d = = 2 2 ( ) ( τ) τ ( ) τ τ 4 8 C for 4 8. In paricular, q(8) = C. q = i d + q 4 = d + 4= + 4= 4 4

2 ( ) ( ) ( ) q = i d + q 8 = d + = 8 8 C for 8. P.3-2 A charge of 45 nc passes hrough a circui elemen during a paricular inerval of ime ha is 5 ms in duraion. Deermine he average curren in his circui elemen during ha inerval of ime. Answer: i = 9 μa 9 q 45 6 i = = = 9 = 9 ma 3 5 P.3-4 The charge flowing in a wire is ploed in Figure P.3-4. Skech he corresponding curren. Figure P.3-4 P = 7.5 = 7.5 ma when < < 2ms d 5 3 i( ) = q( ) = he slope of he q versus plo = = 5 = 5 ma when 4ms< < 7ms 6 d 3 oherwise P.5- Figure P.5- shows four circui elemens idenified by he leers A, B, C, and D. (a) hich of he devices supply 3 m? (b) hich of he devices absorb.3? (c) ha is he value of he power received by device B? (d) ha is he value of he power delivered by device B? (e) ha is he value of he power delivered by device C?

3 Figure P.5- (a) A and D. The elemen volage and curren do no adhere o he passive convenion in Figures P.5- A and D so he produc of he elemen volage and curren is he power supplied by hese elemens. (b) B and C. The elemen volage and curren adhere o he passive convenion in Figures P.5- B and C so he produc of he elemen volage and curren is he power delivered o, or absorbed by hese elemens. (c) 3 m. The elemen volage and curren adhere o he passive convenion in Figure P.5-B, so he produc of he elemen volage and curren is he power received by his elemen: (5 V)(6 ma) = 3 m. The power supplied by he elemen is he negaive of he power received o he elemen, 3. (d) 3 m (e) 3 m. The elemen volage and curren adhere o he passive convenion in Figure P.5-C, so he produc of he elemen volage and curren is he power received by his elemen: (5 V)(6 ma) = 3 m. The power supplied by he elemen is he negaive of he power received o he elemen, 3. P.5-3 A walker s cassee ape player uses four AA baeries in series o provide 6 V o he player circui. The four alkaline baery cells sore a oal of 2 wa-seconds of energy. If he cassee player is drawing a consan ma from he baery pack, how long will he cassee operae a normal power? ( )( ) P = 6V ma =.6 w 2 s = = = P s P.5-5 An auomobile baery is charged wih a consan curren of 2 A for five hours. The erminal volage of he baery is v = +.5 V for >, where is in hours. (a) Find he energy delivered o he baery during he five hours. (b) If elecric energy coss 5 cens/kh, find he cos of charging he baery for five hours.

4 Answer: (b).84 cens a.) Assuming no more energy is delivered o he baery afer 5 hours (baery is fully charged). 5( 36) 5( 36) w = Pd = vi d = 2 22 d + = = 44 J = 44 kj b.) hr 5 Cos = 44kJ =.84 36s khr

5 P.5-6 Find he power, p(), supplied by he elemen shown in Figure P.5-6 when v() = 4 sin 3 V and i() = (/2) sin 3 A. Evaluae p() a =.5 s and = s. Observe ha he power supplied by his elemen has a posiive value a some imes and a negaive value a oher imes. Hin: (sin a)(sin b) = (cos( a b) cos( a + b) ) 2 Answer: p() = (/6)cos(6), p(.5) =.235, p() =.2466 p ( ) vi ( ) ( ) ( 4cos3) = = sin 3 = ( sin + sin 6) = sin p (.5) = sin 3 = p ( ) = sin 6 = Here is a MATLAB program o plo p(): clear =; % iniial ime f=2; % final ime d=.2; % ime incremen =:d:f; % ime v=4*cos(3*); i=(/2)*sin(3*); for k=:lengh() p(k)=v(k)*i(k); end % device volage % device curren % power plo(,p) xlabel('ime, s'); ylabel('power, ')

6 P.5-7 Find he power, p(), supplied by he elemen shown in Figure P.5-6 when v() = 8 sin 3 V and i() = 2 sin 3 A. Hin: (sin a)(sin b) = (cos( a b) cos( a + b) ) 2 Answer: p() = 8 8cos 6 Figure P.5-7 ( ) ( ) ( ) ( )( ) ( ) p = vi = 8sin 3 2sin 3 = 8 cos cos 6 = 8 8cos 6 Here is a MATLAB program o plo p(): clear =; f=2; d=.2; =:d:f; v=8*sin(3*); i=2*sin(3*); for k=:lengh() p(k)=v(k)*i(k); end % iniial ime % final ime % ime incremen % ime % device volage % device curren % power plo(,p) xlabel('ime, s'); ylabel('power, ')

7 P.5-8 Find he power, p(), supplied by he elemen shown in Figure P.5-6. The elemen volage is represened as v() = 4( e 2 )V when and v() = when <. The elemen curren is represened as i() = 2e 2 A when and i() = when <. Answer: p() = 8( e 2 )e 2 Here is a MATLAB program o plo p(): clear ( ) = ( ) ( ) = ( ) = ( ) p vi e e e e Figure P.5-7 =; f=2; d=.2; =:d:f; v=4*(-exp(-2*)); i=2*exp(-2*); for k=:lengh() p(k)=v(k)*i(k); end % iniial ime % final ime % ime incremen % ime % device volage % device curren % power plo(,p) xlabel('ime, s'); ylabel('power, ')