(6)(2) (-6)(-4) (-4)(6) + (-2)(-3) + (4)(3) + (2)(-3) = = 0

Transcription

1 Chapter 3 Homework Soluton P3.-, 4, 6, 0, 3, 7, P3.3-, 4, 6, P3.4-, 3, 6, 9, P3.5- P3.6-, 4, 9, 4,, 3, P 3.- Determne the alues of, 4,, 3, and 6 n Fgure P 3.-. Apply KCL at node a to get Apply KCL at node b to get = + 6 = 0 = 4 A 3 = = -3 A Apply KVL to the loop consstng of elements A and B to get - 6 = 0 = -6 V Apply KVL to the loop consstng of elements C, D, and A to get - 3 (-) 6 = 0 4 = -4 V Apply KVL to the loop consstng of elements E, F and D to get (-) = 0 6 = V Check: The sum of the power suppled by all branches s (6)() (-6)(-4) (-4)(6) + (-)(-3) + (4)(3) + ()(-3) = = 0

2 P 3.-4 Determne the power absorbed by each of the resstors n the crcut shown n Fgure P soluton Power absorbed by the 4 resstor = 4 = 00 W Power absorbed by the 6 resstor = 6 = 4 W Power absorbed by the 8 resstor = 8 = 7 W 4 A A 4 3 A 3 3 A 4 3 (checked usng LNAP 8/6/0) P 3.-6 Determne the power suppled by each oltage source n the crcut of Fgure P Answer: The -V oltage source supples mw and the 3-V oltage source supples 6 mw.

3 Fgure P P ma mw 3 3 P ma mw (checked usng LNAP 8/6/0) P 3.-0 The crcut shown n Fgure P 3.-0 conssts of fe oltage sources and four current sources. Express the power suppled by each source n terms of the oltage source oltages and the current source currents. Fgure P 3.-0 The subscrpts suggest a numberng of the sources. Apply KVL to get and do not adhere to the passe conenton, so p 5 9 6

4 s the power suppled by source. Next, apply KCL to get 4 and do not adhere to the passe conenton, so p 4 s the power suppled by source. Next, apply KVL to get 3 and 3 adhere to the passe conenton, so p s the power suppled by source 3. Next, apply KVL to get and 4 do not adhere to the passe conenton, so p s the power suppled by source 4. Next, apply KCL to get 5 and 5 adhere to the passe conenton, so p s the power suppled by source 5. Next, apply KCL to get 6 and 6 adhere to the passe conenton, so p s the power suppled by source 6. Next, apply KVL to get 7 and 7 adhere to the passe conenton, so 7 6 p s the power suppled by source 7. Next, apply KCL to get

5 8 4 8 and 8 do not adhere to the passe conenton, so p s the power suppled by source 8. Fnally, apply KCL to get 9 and 9 adhere to the passe conenton, so s the power suppled by source p (Check: 9 p n 0.) n P 3.-3 Determne the alue of the current that s measured by the meter n Fgure P We can label the crcut as shown. The subscrpts suggest a numberng of the crcut elements. Apply KVL to node the left mesh to get Fgure P A 40 Apply KVL to node the left mesh to get V

6 Apply KCL to get m. Fnally, apply Ohm s law to the 50 resstor to get A m (Checked: LNAPDC 9//04) P 3.-7 Determne the current n Fgure P Answer: = 4 A Fgure P Apply KCL at node a to determne the current n the horzontal resstor as shown. Apply KVL to the loop consstng of the oltages source and the two resstors to get -4(-) + 4() - 4 = 0 = 4 A P3.- Determne the alue of the oltage 5 for the crcut shown n Fgure P3.-. Fgure P3.-

7 Apply KVL to the left mesh: V Use the element equaton of the dependent source: A Apply KCL at the rght node V 5 P 3.3- Consder the crcuts shown n Fgure P (a) Determne the alue of the resstance n Fgure P 3.3-b that makes the crcut n Fgure P 3.3-b equalent to the crcut n Fgure P 3.3-a. (b) Determne the current n Fgure P 3.3-b. Because the crcuts are equalent, the current n Fgure P 3.3-a s equal to the current n Fgure P 3.3-b. (c) Determne the power suppled by the oltage source. ( a) ( b).867 A 5 c p 8 =8(.867)=5.7 W (8 V and do not adhere to the passe conenton.)

8 P Determne the oltage n the crcut shown n Fgure P Fgure P Voltage dson V V KVL: V (checked usng LNAP 8/6/0) P The nput to the crcut shown n Fgure P s the oltage of the oltage source, a. The output of ths crcut s the oltage measured by the oltmeter, b. Ths crcut produces an output that s proportonal to the nput, that s where k s the constant of proportonalty. b = k a (a) Determne the alue of the output, b, when = 40 Ω and a = 8 V. (b) (c) (d) Determne the alue of the power suppled by the oltage source when = 40 Ω and a = 8 V. Determne the alue of the resstance,, requred to cause the output to be b = V when the nput s a = 8 V. Determne the alue of the resstance,, requred to cause b = 0. a (that s, the alue of the constant of proportonalty s k ). 0

9 Fgure P a.) V b.) 8.08 W 0 80 c.) d.) P 3.3- For the crcut of Fgure P 3.3-, fnd the oltage 3 and the current and show that the power delered to the three resstors s equal to that suppled by the source. Fgure P 3.3-

10 3 From oltage dson 3 3 V 39 then = 3 = A W The power absorbed by the resstors s: The power suppled by the source s ()() = W. P 3.4- Use current dson to determne the currents,, 3, and 4 n the crcut shown n Fgure P Fgure P A A; A A P The deal oltmeter n the crcut shown n Fgure P measures the oltage.

11 Fgure P (a) Suppose = Ω. Determne the alue of and of the current. (b) Suppose, nstead, = Ω. Determne the alue of and of the current. (c) Instead, choose and to mnmze the power absorbed by any one resstor. 8 8 or ( ) or 8 8 a A ; b A ; wll cause = A. The current n both and wll be A. 8 ; c P Fgure P shows a transstor amplfer. The alues of and are to be selected. esstances and are used to bas the transstor, that s, to create useful operatng condtons. In ths problem, we want to select and so that b = 5 V. We expect the alue of b to be approxmately 0 μa. When 0 b, t s customary to treat b as neglgble, that s, to assume b = 0. In that case and comprse a oltage dder.

12 (a) (b) Fgure P Select alues for and so that b = 5 V and the total power absorbed by and s no more than 5 mw. An nferor transstor could cause b to be larger than expected. Usng the alues of and from part (a), determne the alue of b that would result from b = 5 μa. (a) To nsure that b s neglgble we requre so 50 k To nsure that the total power absorbed by and s no more than 5 mw we requre k Next to cause b = 5 V we requre 5 5 b For example, 40 k, 80 k, satsfy all three requrements. (b) 3 KVL ges b b 6 KCL ges b 6 Therefore b Fnally 3.8 3b. 5 b 4.6 V 3

13 P Determne the power suppled by the dependent source n Fgure P Use current dson to get a so ma b V Fgure P The power suppled by the dependent source s gen by 3 p mw P 3.4- Determne the alue of the current measured by the meter n Fgure P eplace the (deal) ammeter wth the equalent short crcut. Label the current measured by the meter. Fgure P 3.4-

14 Apply KCL at the left node of the VCCS to get a.. 0. a 0.3 a a 4 V Use current dson to get m a A P 3.5- Determne the power suppled by each source n the crcut shown n Fgure P Fgure P 3.5- The 0- and 5- resstors are connected n parallel. The equalent resstance s The 7- resstor s connected n parallel wth a short crcut, a 0- resstor. The equalent resstance s 0 7 0, a short crcut. 0 7 The oltage sources are connected n seres and can be replaced by a sngle equalent oltage source. After dong so, and labelng the resstor currents, we hae the crcut shown.

15 The parallel current sources can be replaced by an equalent current source. Apply KVL to get V The power suppled by each sources s: Source Power delered 8-V oltage source W 3-V oltage source W 3-A current source W 0.5-A current source W (Checked usng LNAP, 9/5/04) P 3.6- The crcut shown n Fgure P 3.6-a has been dded nto two parts. In Fgure P 3.6-b, the rght-hand part has been replaced wth an equalent crcut. The left-hand part of the crcut has not been changed. (a) (b) (c) Determne the alue of the resstance n Fgure P 3.6-b that makes the crcut n Fgure P 3.6- b equalent to the crcut n Fgure P 3.6-a. Fnd the current and the oltage shown n Fgure P 3.6-b. Because of the equalence, the current and the oltage shown n Fgure P 3.6-a are equal to the current and the oltage shown n Fgure P 3.6-b. Fnd the current shown n Fgure Fgure P 3.6-

16 P 3.6-a usng current dson. a b V ; A 3 c 48 A P (a) Determne alues of and n Fgure P 3.6-4b that make the crcut n Fgure P 3.6-4b equalent to the crcut n Fgure P 3.6-4a. (b) (c) Analyze the crcut n Fgure P 3.6-4b to determne the alues of the currents a and b Because the crcuts are equalent, the currents a and b shown n Fgure P 3.6-4b are equal to the currents a and b shown n Fgure P 3.6-4a. Use ths fact to determne alues of the oltage and current shown n Fgure P 3.6-4a. Fgure P 3.6-4

17 (a) 4 and 4 8 (b) (c) Frst, apply KVL to the left mesh to get 7 6a 3a 0 a 3 A. Next, apply KVL to the left mesh to get A. b a b P Determne the alue of the current n Fgure Answer: = 0.5 ma Fgure 3.6-9

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19 P All of the resstances n the crcut shown n Fgure P are multples of. Determne the alue of. So the crcut s equalent to Fgure P

20 Then P 3.6- Determne the alue of the resstance n the crcut shown n Fgure P 3.6-, gen that eq = 9 Ω. Answer: = 5 Ω eplace parallel resstors by an equalent resstor: 8 4 = 6 Fgure P 3.6- A short crcut n parallel wth a resstor s equalent to a short crcut. eplace seres resstors by an equalent resstor: 4+6 = 0

21 Now so eq P The oltmeter n Fgure P measures the oltage across the current source. (a) (b) Fgure P Determne the alue of the oltage measured by the meter. Determne the power suppled by each crcut element. eplace the deal oltmeter wth the equalent open crcut and label the oltage measured by the meter. Label the element oltages and currents as shown n (b). Usng unts of V, A, and W: a.) Determne the alue of the oltage measured by the meter. Krchhoff s laws ge Usng unts of V, ma, k and mw: a.) Determne the alue of the oltage measured by the meter. Krchhoff s laws ge

22 and Ohm s law ges Then m 3 s 0 A V m 50 6 V 3 and s ma m Ohm s law ges Then m V 50 6 V b.) Determne the power suppled by each element. oltage source 3 s W current source resstor total W W b.) Determne the power suppled by each element. oltage source current source s 4 mw 6 4 mw resstor total mw P Consder the crcut shown n Fgure P Gen that the oltage of the dependent oltage source s a 8 V, determne the alues of and o. Fgure P3.6-40

23 Frst, Next, 0 o 8 3. V b then c 40 40