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hw7 - wilson(kw22588 HW7 Mackie(20224 This print-out should...

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wilson (kw22588) – HW7 – Mackie – (20224) 1 This print-out should have 16 questions. Multiple-choice questions may continue on the next column or page – find all choices before answering. 001 10.0 points The current in a wire decreases with time according to the relationship I = (2 . 15 mA) × e - at where a = 0 . 13328 s - 1 . Determine the total charge that passes through the wire from t = 0 to the time the current has diminished to zero. Correct answer: 0 . 0161315 C. Explanation: I = dq dt q = integraldisplay t t =0 I dt = integraldisplay t =0 (0 . 00215 A) e - 0 . 13328 s - 1 t dt = (0 . 00215 A ) e - 0 . 13328 s - 1 t - 0 . 13328 s - 1 vextendsingle vextendsingle vextendsingle vextendsingle vextendsingle 0 = 0 . 0161315 C . 002 10.0 points The total charge that an automobile battery can supply without being recharged is given in terms of Ampere-hours. A typical 12-V battery has a rating of 42 A · h . Suppose you forget to turn off the headlights in your parked automobile. If each of the two headlights draws 3 . 9 A , find out the time before your battery is “dead”. Correct answer: 5 . 38462 h. Explanation: Let : rating = 42 A · h and I = 3 . 9 A . If only one of the two headlights is left on, the time before the battery dies is given by T 1 = rating I = 42 A · h 3 . 9 A = 10 . 7692 h . Thus the required time is 5 . 38462 h . 003 (part 1 of 2) 10.0 points The quantity of charge passing through a sur- face of area 1 . 71 cm 2 varies with time as q = q 1 t 3 + q 2 t + q 3 , where q 1 = 3 . 2 C / s 3 , q 2 = 3 . 7 C / s, q 3 = 5 . 1 C, and t is in seconds. What is the instantaneous current through the surface at t = 0 . 7 s? Correct answer: 8 . 404 A. Explanation: Let : q 1 = 3 . 2 C / s 3 , q 2 = 3 . 7 C / s , q 3 = 5 . 1 C , and t = 0 . 7 s . I d q dt = 3 q 1 t 2 + q 2 = 3 ( 3 . 2 C / s 3 ) (0 . 7 s) 2 + 3 . 7 C / s = 8 . 404 A . 004 (part 2 of 2) 10.0 points What is the value of the current density at t = 0 . 7 s? Correct answer: 49146 . 2 A / m 2 . Explanation: Let : a = 1 . 71 cm 2 = 0 . 000171 m 2 and t = 0 . 7 s .
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wilson (kw22588) – HW7 – Mackie – (20224) 2 J I A = 8 . 404 A 0 . 000171 m 2 = 49146 . 2 A / m 2 .
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