Chapter Homework Solution P.-1,, 5 P.4-1, 3, 5, 6, 7 P.5-1, 3, 5 P.6-, 5 P.7-1, 4 P.8-1 P.9-1 P.-1 An element ha oltage and current i a hown in Figure P.-1a. Value of the current i and correponding oltage hae been tabulated a hown in Figure P.-1b. Determine if the element i linear. Figure P.-1 The element i not linear. For example, doubling the current from A to 4 A doe not double the oltage. Hence, the property of homogeneity i not atified. P.- A linear element ha oltage and current i a hown in Figure P.-a. Value of the current i and correponding oltage hae been tabulated a hown in Figure P.-b. epreent the element by an equation that expree a a function of i. Thi equation i a model of the element. (a) Verify that the model i linear. (b) Ue the model to predict the alue of correponding to a current of i = 40 ma. (c) Ue the model to predict the alue of i Figure P.-a correponding to a oltage of = 4 V. Hint: Plot the data. We expect the data point to lie on a traight line. Obtain a linear model of the element by repreenting that traight line by an equation. (a) The data point do indeed lie on a traight line. The lope of the line i 0.1 V/A and the line pae through the origin o the equation of the line i = 0.1i. The element i indeed linear. (b) When i = 40 ma, = (0.1 V/A) (40 ma) = (0.1 V/A) (0.04 A) = 4.8 mv 3 (c) When = 3 V, i = = 5 A 0.1
P.-5 The circuit hown in Figure P.3-5 conit of a current ource, a reitor, and element A. Conider three cae. (a) Figure P.3-5 When element A i a 40-Ω reitor, decribed by i = / 40, then the circuit i repreented by 0.4 = + 10 40 Determine the alue of and i. Notice that the aboe equation ha a unique olution. (b) When element A i a nonlinear reitor decribed by i = /, then the circuit i repreented by 0.4 = + 10 Determine the alue of and i. In thi cae there are two olution of the aboe equation. Nonlinear circuit exhibit more complicated behaior than linear circuit. (c) When element A i a nonlinear reitor decribed by i = 0.8+, then the circuit i decribed by 0.4 = + 0.8 + 10 Show that thi equation ha no olution. Thi reult uually indicate a modeling problem. At leat one of the three element in the circuit ha not been modeled accurately. (a) 0.4 = + = 10 40 8 = 3. V i = = 0.08 A 40 0.4 = + + 0.8 = 0 (b) 10 5 0. ± 1.8 Uing the quadratic formula = = 0.8, 1.0 V 0.8 ( 1) When = 0.8 V then i = = 0.3 A. When = -1.0 V then i = = 0.5 A. (c) 0.4 = + 0.8 + + + 0.8 = 0 10 5 0. ± 0.04 3. Uing the quadratic formula = So there i no real olution to the equation. P.4-1 A current ource and a reitor are connected in
erie in the circuit hown in Figure P.4-1. Element connected in erie hae the ame current, o i = i in thi circuit. Suppoe that i = 3 A and = 7 Ω. Calculate the oltage acro the reitor and the power aborbed by the reitor. Anwer: = 1 V and the reitor aborb 63 W. Figure P.4-1 i = i = 3 A and = i = 7 3 = 1 V and i adhere to the paie conention P = i = 1 3 = 63 W i the power aborbed by the reitor. P.4-3 A oltage ource and a reitor are connected in parallel in the circuit hown in Figure P.4-3. Element connected in parallel hae the ame oltage, o = in thi circuit. Suppoe that = 10 V and = 5 Ω. Calculate the current i in the reitor and the power aborbed by the reitor. Anwer: i = A and the reitor aborb 0 W. Figure P.4-3 = =10 V and = 5 W 10 i = = = A 5 and i adhere to the paie conention p = i = 10 = 0 W i the power aborbed by the reitor P.4-5 A oltage ource and two reitor are connected in parallel in the circuit hown in Figure P.4-5. Element connected in parallel hae the ame oltage, o 1 = and = in thi circuit. Suppoe that = 150 V, 1 = 50 Ω, and = 5 Ω. Calculate the current in each reitor and the power aborbed by each reitor. Hint: Notice the reference direction of the reitor current. Figure P.4-5 Anwer: i 1 = 3 A and i = 6 A. 1 aborb 450 W and aborb 900 W.
1 i = = = 150 V; = 50 Ω ; = 5 Ω 1 and i 1 1 i i 1 1 = = = 1 50 adhere to the paie conention o 150 3 A and do not adhere to the paie conention o = = = 6 A 5 The power aborbed by i P = i = 150 3 = 450 W 1 1 1 1 The power aborbed by i P = i = 150( 6) = 900 W 150 P.4-6 A current ource and two reitor are connected in erie in the circuit hown in Figure P.4-6. Element connected in erie hae the ame current, o i 1 = i and i = i in thi circuit. Suppoe that i = A, 1 = 4 Ω, and = 8 Ω. Calculate the oltage acro each reitor and the power aborbed by each reitor. Hint: Notice the reference direction of the reitor oltage. Figure P.4-6 Anwer: 1 = 8 V and = 16 V. 1 aborb 16 W and aborb 3 W. i = i = i =5 ma and = 4 W and = 8 W 1 1 and i 1 1 1 1 1 1 1 1 do not adhere to the paie conention o ( ) = i = 4 0.05 = 0.1 V. The power aborbed by P= i = ( 0.1)(0.05) =.5 mw. 1 i ( ) and i do adhere to the paie conention o = i = 8 0.05 = 0. V. The power aborbed by i P = i =(0.)(0.05) = 5 mw. P.4-7 An electric heater i connected to a contant 50-V ource and aborb 1000 W. Subequently, thi heater i connected to a contant 10-V ource. What power doe it aborb from the 10-V ource? What i the reitance of the heater? Hint: Model the electric heater a a reitor.
(50) Model the heater a a reitor, then from P= = = P 1000 = 6.5 W with a 0 V ource (0) P = = = 774.4 W 6.5 P.5-1 A current ource and a oltage ource are connected in parallel with a reitor a hown in Figure P.5-1. All of the element connected in parallel hae the ame oltage, in thi circuit. Suppoe that = 15 V, i = 3 A, and = 5 Ω. (a) Calculate the current i in the reitor and the power aborbed by the reitor. (b) Change the current ource current to i = 5 A and recalculate the current, i, in the reitor and the power aborbed by the reitor. Anwer: i = 3 A and the reitor aborb 45 W both when i = 3 A and when i = 5 A. Figure P.5-1 (a) i 15 = = = 3 A and P = i = 5 5 ( 3 ) = 45 W (b) i and P do not depend on i. The alue of i and P are 3 A and 45 W, both when i = 3 A and when i = 5 A. P.5-3 The current ource and oltage ource in the circuit hown in Figure P.5-3 are connected in parallel o that they both hae the ame oltage,. The current ource and oltage ource are alo connected in erie o that they both hae the ame current, i. Suppoe that = 1 V and i = 3 A. Calculate the power upplied by each ource. Anwer: The oltage ource upplie 36 W, and the current ource upplie 36 W. Figure P.5-3
Conider the current ource: i and do not adhere to the paie conention, o P = i = 3 1 = 36 W c i the power upplied by the current ource. Conider the oltage ource: i and do adhere to the paie conention, o P = i = 3 1 = 36 W i the power aborbed by the oltage ource. The oltage ource upplie 36 W. P.5-5 (a) Find the power upplied by the oltage ource hown in Figure P.5-5 when for t 0 we hae and (b) = cotv i= 10 cot ma Determine the energy upplied by thi oltage ource for the period 0 t 1. Figure P.5-5 (a) (b) P= i= t t = t ( co ) (10 co ) 0 co mw 1 1 1 1 1 0 co = 0 in 10 5 in mj 0 0 4 0 w = P dt = t dt t+ t = + P.6- The current ource in Figure P.6- upplie 40 W. What alue do the meter in Figure P.6- read?
Figure P.6- The oltmeter current i zero o the ammeter current i equal to the current ource current except for the reference direction: i = - A The oltage i the oltage of the current ource. The power upplied by the current ource i 40 W o 40 = = 0 V
P.6-5 The oltmeter in Figure P.6-5a meaure the oltage acro the current ource. Figure P.6-5b how the circuit after remoing the oltmeter and labeling the oltage meaured by the oltmeter a m. Alo, the other element oltage and current are labeled in Figure P.6-5b. Gien that 1= + and i = i = A m and = 5i (a) (b) Determine the alue of the oltage meaured by the meter. Determine the power upplied by each element. a.) ( ) = 5 i = 5 = 50 V Figure P.6-5 m ( ) = 1 = 1 50 = 6 V b.) Element Power upplied oltage ource ( i ) ( ) 1 = 1 = 4 W current ource 6( ) = 14 W reitor i ( )( ) = 50 = 100 W total 0
P.7-1 The ammeter in the circuit hown in Figure P.7-1 indicate that i a = A, and the oltmeter indicate that b = 8 V. Determine the alue of r, the gain of the CCVS. Anwer: r = 4 V/A Figure P.7-1 r b 8 = = = 4 Ω i a P.7-4 The oltmeter in the circuit hown in Figure P.7-4 indicate that a = V and b = 8 V. Determine the alue of b, the gain of the VCVS. Anwer: b = 4 V/V Figure P.7-4 b 8 V a = V ; ba = b = 8 V ; b = = = 4 V a
P.8-1 For the potentiometer circuit of Figure.8-, the current ource current and potentiometer reitance are 1.1 ma and 100 kω, repectiely. Calculate the required angle, θ, o that the meaured oltage i 3 V. Figure.8- θ 360 m (360)(3 V) a =, θ = = = 75.7 360 i (100 kω)(1.1 ma) p P.9-1 Determine the current, i, at t = 1 and at t = 4 for the circuit of Figure P.9-1. Figure P.9-1 At t = 1 the left witch i open and the right witch i cloed o the oltage acro the reitor i 10 V. 10 i = = = ma 3 5 10 At t = 4 the left witch i cloed and the right witch i open o the oltage acro the reitor i 15 V. 15 i = = = 3 ma 3 5 10