Homework_05-solutions - toupal(rgt374 Homework 05...

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toupal (rgt374) – Homework 05 – Chiu – (58295) 1 This print-out should have 14 questions. Multiple-choice questions may continue on the next column or page – find all choices before answering. 001 (part 1 of 2) 10.0 points The quantity of charge passing through a sur- face of area 2 . 29 cm 2 varies with time as q = q 1 t 3 + q 2 t + q 3 , where q 1 = 5 . 2 C / s 3 , q 2 = 4 . 1 C / s, q 3 = 9 . 4 C, and t is in seconds. What is the instantaneous current through the surface at t = 1 . 4 s? Correct answer: 34 . 676 A. Explanation: Let : q 1 = 5 . 2 C / s 3 , q 2 = 4 . 1 C / s , q 3 = 9 . 4 C , and t = 1 . 4 s . I d q dt = 3 q 1 t 2 + q 2 = 3 ( 5 . 2 C / s 3 ) (1 . 4 s) 2 + 4 . 1 C / s = 34 . 676 A . 002 (part 2 of 2) 10.0 points What is the value of the current density at t = 1 . 4 s? Correct answer: 1 . 51424 × 10 5 A / m 2 . Explanation: Let : a = 2 . 29 cm 2 = 0 . 000229 m 2 and t = 1 . 4 s . J I A = 34 . 676 A 0 . 000229 m 2 = 1 . 51424 × 10 5 A / m 2 . 003 (part 1 of 3) 10.0 points Consider two cylindrical conductors made of the same ohmic material. Conductor 1 has a radius r 1 and length 1 while conductor 2 has a radius r 2 and length 2 . Denote: The currents of the two conductors as I 1 and I 2 , the potential differences between the two ends of the conductors as V 1 and V 2 , and the electric fields within the conductors as E 1 and E 2 . V 1 vector E 1 I 1 1 r 1 V 2 vector E 2 I 2 2 r 2 If ρ 2 = ρ 1 , r 2 = 2 r 1 , ℓ 2 = 3 1 and V 2 = V 1 , find the ratio R 2 R 1 of the resistances. 1. R 2 R 1 = 3 4 correct 2. R 2 R 1 = 1 2 3. R 2 R 1 = 2 3 4. R 2 R 1 = 3 2 5. R 2 R 1 = 1 4 6. R 2 R 1 = 3 7. R 2 R 1 = 2 8. R 2 R 1 = 4 9. R 2 R 1 = 1 3 10. R 2 R 1 = 4 3 Explanation:
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toupal (rgt374) – Homework 05 – Chiu – (58295) 2 The relation between resistance and resis- tivity is given by R = ρ ℓ A = ρ ℓ π r 2 . Then since r 2 = 2 r 1 and 2 = 3 1 , the ratio of the resistances is R 2 R 1 = ρ ℓ 2 π r 2 2 π r 2 1 ρ ℓ 1 = 2 r 2 1 1 r 2 2 = (3 1 ) r 2 1 1 (2 r 1 ) 2 = 3 4 . 004 (part 2 of 3) 10.0 points When the two conductors are attached to a battery of voltage V, determine the ratio E 2 E 1 of the electric fields.
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