chapter 07 - Chapter 7 Energy Storage Elements Exercises...

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Chapter 7 Energy Storage Elements Exercises Ex. 7.3-1 () 22 4 11 4 0o t h e r w i s e Cs t d it vt t dt << == < 8 < 8 e and () () 242 4 18 4 t h e r w i s Rs tt t t = =− < < so 222 4 7 4 8 t h e r w i s CR i t i t t t −< < =+= − < < e Ex. 7.3-2 0 0 0 ( ) 12 1 3 ss t i d i d C ττ =+ = ∫∫ < < 0 ( ) 3 4 12 12 12 for 0 4 t d t t τ = < In particular, v (4) = 36 V. 4 ( ) 3 2 36 60 6 for 4 10 t d t t =− + < < In particular, v (10) = 0 V. 10 () 3 0 0 0 fo r 10 t d t = Ex. 7.4-1 2 2 4 1 2 10 100 1 J 2 2 0 0 100 V cc Cv vv +− × = W 7-1
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Ex. 7.4-2 a) b) () ( ) () () () 0 44 00 0 0 F i r s t , 0 0 s i n c e 1 Next, 0 10 2 2 10 210 2 2 10 t tt t tv i d t v v t v i dt dt t C d t t =+ == = = × 2 = × ∫∫ WW W 4 1s 2 10 J = 20 kJ W () ( ) 2 48 100s 2 10 100 2 10 J = 200 MJ W Ex. 7.4-3 a) b) 55 5 We have (0 ) (0 ) 3 V 1 (0 ) 5 3 3 3 1 3 3 V , 0 1 t cc vv v t i t dt v e dt e e t C +− = + = + = < < () () ( ) ( ) 5 5 15 3 18 V , 0 1 t Rc c v t vt vt i t vt e e e t =+=+=+= < < 2 0.2 25 1 0 0.8 ( ) 6.65 J 11 0.2 3 0.9 J 22 2.68 kJ ts c t tC v t e e t = = = × = ⇒ = W W W Ex. 7.5-1 7-2
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Ex. 7.5-2 12 1 2 1 1 2 dv dv i i C vv i i dt dt C C C =⇒ = ⇒ =⇒= 2 KCL: 2 2 21 1 CC iii i i  =+= + =  +  2 i C Ex. 7.5-3 (a) to (b) : 11 mF 111 9 + + 333 = , (b) to (c) : 0 = mF 99 1+ , (c) to (d) : 1111 1 0 = + + = mF 10 22 1 9 9 eq eq C C 7-3
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Ex. 7.6-1 () 22 4 11 4 0o t h e r w i s Ls t d vt it t dt << == < 8 e < 8 e and () () 242 4 18 4 t h e r w i s Rs tt t t = =− < < so 222 4 7 4 8 t h e r w i s LR v t v t t t −< < =+= < e Ex. 7.6-2 0 0 0 ( ) 12 1 3 ss t v d v d L ττ =+ = ∫∫ < < 0 ( ) 3 4 12 12 12 for 0 4 t d t t τ = < In particular, i (4) = 36 A. 4 ( ) 3 2 36 60 6 for 4 10 t d t t =− + = < < In particular, i (10) = 0 A. 10 () 3 0 0 0 fo r 10 t d t = Ex. 7.7-1 ()() () 2 2 2 1 4 1 V 4 1 4 4 1 W 1 42 J 4 di d vL t e t e dt dt Pv i t e t e t t e Li t e t e −−  =    == − =  = W t 7-4
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Ex. 7.7-2 () 0 0 00 2 0 1 10 1 and 2212 21 02 2 t t tt t di di vt L it dt dt t t t < < << 1 1 2 < <  == = ⇒=  −− < < > > () ()() 0 1 221 t pt vtit t < −< < > 0 2 2 () ( ) ( ) () ( ) 0 0 0 ( ) 0 for 0 0 for 0 0 t t p t d t t p t t t =+ =< WW W = () () ( ) 2 0 2 1 01 : 2 12 : 1 22 4 2 : 0 t t ttt d t t t d t t t = = = + = + >= = 4 Ex. 7.8-1 7-5
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Ex. 7.8-2 Ex. 7.8-3 () () () () 00 1 10 2 20 12 11 , but 0 and 0 tt i v dt i t i v dt i t i t i t LL =+ =+ = ∫∫ = 0 0 0 0 2 1 + 1 + t t t t P t t t t P i i i v dt v dt v dt v dt L vdt iL L L  =+= + = =   1 L == = + 7-6
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