PROPRIETARY MATERIAL. © 2007 The McGraw-Hill Companies, Inc. All rights reserved. No part of this Manual may be displayed, reproduced or distributed in any form or by any means, without the prior written permission of the publisher, or used beyond the limited distribution to teachers and educators permitted by McGraw-Hill for their individual course preparation. If you are a student using this Manual, you are using it without permission. Chapter 1, Problem 1 How many coulombs are represented by these amounts of electrons: (a) 6.482×1017 (b) 1.24×1018 (c) 2.46×1019 (d) 1.628×1020 Chapter 1, Solution 1 (a) q = 6.482x1017x [-1.602x10-19C] = -0.10384 C (b) q = 1. 24x1018x [-1.602x10-19C] = -0.19865 C (c) q = 2.46x1019x [-1.602x10-19C] = -3.941 C (d) q = 1.628x1020x [-1.602x10-19C] = -26.08 C Chapter 1, Problem 2. Determine the current flowing through an element if the charge flow is given by (a) q(t)=(3t+8) mC (b) q(t)=(8t2 +4t-2) C ( ) ( ) -t −2t (c) q t = 3e −5e nC (d) q(t)=10sin120π t pC (e) q(t)= 20e−4t cos50t μC Chapter 1, Solution 2 (a) i = dq/dt = 3 mA (b) i = dq/dt = (16t + 4) A (c) i = dq/dt = (-3e-t + 10e-2t) nA (d) i=dq/dt = 1200πcos120πt pA (e) i =dq/dt = −e−4t(80cos50t+1000sin50t) μA PROPRIETARY MATERIAL. © 2007 The McGraw-Hill Companies, Inc. All rights reserved. No part of this Manual may be displayed, reproduced or distributed in any form or by any means, without the prior written permission of the publisher, or used beyond the limited distribution to teachers and educators permitted by McGraw-Hill for their individual course preparation. If you are a student using this Manual, you are using it without permission. Chapter 1, Problem 3. Find the charge q(t) flowing through a device if the current is: (a) i(t)=3A, q(0)=1C (b) i(t) = (2t +5)mA,q(0) = 0 (c) i(t) = 20cos(10t +π/6)μA, q(0) = 2 μ C (d) i(t)=10e−30t sin40tA, q(0) =0 Chapter 1, Solution 3 (a) q(t) = ∫i(t)dt+q(0) =(3t +1) C (b) q(t) = ∫(2t+s) dt+q(v) = (t2 +5t) mC (c) q(t)= ∫20 cos (10t+π/6)+q(0)=(2sin(10t+π/6)+1)μC 10e-30t q(t) = ∫10e-30t sin40t+q(0) = (−30sin40t-40 cos t) (d) 900+1600 = −e-30t(0.16cos40t +0.12 sin 40t) C Chapter 1, Problem 4. A current of 3.2 A flows through a conductor. Calculate how much charge passes through any cross-section of the conductor in 20 seconds. Chapter 1, Solution 4 q = it = 3.2 x 20 = 64 C Chapter 1, Problem 5. Determine the total charge transferred over the time interval of 0 ≤ t ≤ 10s when 1 i(t)= t A. 2 Chapter 1, Solution 5 101 t2 10 q = ∫idt = ∫ tdt = =25 C 2 4 0 0 PROPRIETARY MATERIAL. © 2007 The McGraw-Hill Companies, Inc. All rights reserved. No part of this Manual may be displayed, reproduced or distributed in any form or by any means, without the prior written permission of the publisher, or used beyond the limited distribution to teachers and educators permitted by McGraw-Hill for their individual course preparation. If you are a student using this Manual, you are using it without permission. Chapter 1, Problem 6. The charge entering a certain element is shown in Fig. 1.23. Find the current at: (a) t = 1 ms (b) t = 6 ms (c) t = 10 ms Figure 1.23 Chapter 1, Solution 6 dq 80 (a) At t = 1ms, i = = = 40 A dt 2 dq (b) At t = 6ms, i = = 0 A dt dq 80 (c) At t = 10ms, i = = = –20 A dt 4 PROPRIETARY MATERIAL. © 2007 The McGraw-Hill Companies, Inc. All rights reserved. No part of this Manual may be displayed, reproduced or distributed in any form or by any means, without the prior written permission of the publisher, or used beyond the limited distribution to teachers and educators permitted by McGraw-Hill for their individual course preparation. If you are a student using this Manual, you are using it without permission. Chapter 1, Problem 7. The charge flowing in a wire is plotted in Fig. 1.24. Sketch the corresponding current. Figure 1.24 Chapter 1, Solution 7 ⎡25A, 0< t < 2 dq ⎢ i = = -25A, 2< t < 6 dt ⎢ ⎢25A, 6< t <8 ⎣ which is sketched below: PROPRIETARY MATERIAL. © 2007 The McGraw-Hill Companies, Inc. All rights reserved. No part of this Manual may be displayed, reproduced or distributed in any form or by any means, without the prior written permission of the publisher, or used beyond the limited distribution to teachers and educators permitted by McGraw-Hill for their individual course preparation. If you are a student using this Manual, you are using it without permission. Chapter 1, Problem 8. The current flowing past a point in a device is shown in Fig. 1.25. Calculate the total charge through the point. Figure 1.25 Chapter 1, Solution 8 10×1 q = ∫idt = +10×1=15 μC 2 PROPRIETARY MATERIAL. © 2007 The McGraw-Hill Companies, Inc. All rights reserved. No part of this Manual may be displayed, reproduced or distributed in any form or by any means, without the prior written permission of the publisher, or used beyond the limited distribution to teachers and educators permitted by McGraw-Hill for their individual course preparation. If you are a student using this Manual, you are using it without permission. Chapter 1, Problem 9. The current through an element is shown in Fig. 1.26. Determine the total charge that passed through the element at: (a) t = 1 s (b) t = 3 s (c) t = 5 s Figure 1.26 Chapter 1, Solution 9 1 (a) q = ∫idt = ∫10 dt =10 C 0 3 ⎛ 5×1⎞ q = ∫ idt =10×1+⎜10− ⎟+5×1 (b) 0 ⎝ 2 ⎠ =15+7.5+5= 22.5C 5 (c) q = ∫ idt =10+10+10= 30 C 0 Chapter 1, Problem 10. A lightning bolt with 8 kA strikes an object for 15 μ s. How much charge is deposited on the object? Chapter 1, Solution 10 q = it = 8x103x15x10-6 = 120 mC PROPRIETARY MATERIAL. © 2007 The McGraw-Hill Companies, Inc. All rights reserved. No part of this Manual may be displayed, reproduced or distributed in any form or by any means, without the prior written permission of the publisher, or used beyond the limited distribution to teachers and educators permitted by McGraw-Hill for their individual course preparation. If you are a student using this Manual, you are using it without permission. Chapter 1, Problem 11. A rechargeable flashlight battery is capable of delivering 85 mA for about 12 h. How much charge can it release at that rate? If its terminals voltage is 1.2 V, how much energy can the battery deliver? Chapter 1, Solution 11 q= it = 85 x10-3 x 12 x 60 x 60 = 3,672 C E = pt = ivt = qv = 3672 x1.2 = 4406.4 J Chapter 1, Problem 12. If the current flowing through an element is given by ⎧ 3tA, 0 < t < 6s ⎪ ⎪ 18A, 6 < t < 10s i(t)= ⎨ -12 A, 10 < t < 15s ⎪ ⎪⎩ 0, t > 15s Plot the charge stored in the element over 0 < t < 20s. Chapter 1, Solution 12 For 0 < t < 6s, assuming q(0) = 0, t t q(t)=∫idt+q(0)=∫3tdt+0=1.5t2 0 0 At t=6, q(6) = 1.5(6)2 = 54 For 6 < t < 10s, t t q(t)=∫idt+q(6)=∫18dt+54=18t−54 6 6 At t=10, q(10) = 180 – 54 = 126 For 10

Fundamentals of Electric Circuits: Solution Manual

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