hw5 solutions - homework 05 – SMITH TAYLOR – Due 4:00...

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Unformatted text preview: homework 05 – SMITH, TAYLOR – Due: Feb 17 2008, 4:00 am 1 Question 1, chap 27, sect 3. part 1 of 2 10 points The quantity of charge passing through a surface of area 2 . 77 cm 2 varies with time as q = q 1 t 3 + q 2 t + q 3 , where q 1 = 4 . 7 C / s 3 , q 2 = 6 C / s, q 3 = 7 . 9 C, and t is in seconds. What is the instantaneous current through the surface at t = 1 . 2 s? Correct answer: 26 . 304 A (tolerance ± 1 %). Explanation: Let : q 1 = 4 . 7 C / s 3 , q 2 = 6 C / s , q 3 = 7 . 9 C , and t = 1 . 2 s . I ≡ dq dt = 3 q 1 t 2 + q 2 = 3 ( 4 . 7 C / s 3 ) (1 . 2 s) 2 + 6 C / s = 26 . 304 A . Question 2, chap 27, sect 3. part 2 of 2 10 points What is the value of the current density at t = 1 . 2 s? Correct answer: 94960 . 3 A / m 2 (tolerance ± 1 %). Explanation: Let : A = 2 . 77 cm 2 = 0 . 000277 m 2 and t = 1 . 2 s . J ≡ I A = 26 . 304 A . 000277 m 2 = 94960 . 3 A / m 2 . Question 3, chap 27, sect 2. part 1 of 3 10 points Consider two cylindrical conductors made of the same ohmic material. Conductor 1 has a radius r 1 and length ℓ 1 while conductor 2 has a radius r 2 and length ℓ 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 ℓ 1 r 1 b V 2 vector E 2 I 2 ℓ 2 r 2 b If ρ 2 = ρ 1 , r 2 = 2 r 1 , ℓ 2 = 3 ℓ 1 and V 2 = V 1 , find the ratio R 2 R 1 of the resistances. 1. R 2 R 1 = 1 3 2. R 2 R 1 = 4 3 3. R 2 R 1 = 3 2 4. R 2 R 1 = 3 4 correct 5. R 2 R 1 = 4 6. R 2 R 1 = 3 7. R 2 R 1 = 2 3 8. R 2 R 1 = 1 4 9. R 2 R 1 = 2 10. R 2 R 1 = 1 2 homework 05 – SMITH, TAYLOR – Due: Feb 17 2008, 4:00 am 2 Explanation: 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 ℓ 2 = 3 ℓ 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 = ℓ 2 r 2 1 ℓ 1 r 2 2 = (3 ℓ 1 ) r 2 1 ℓ 1 (2 r 1 ) 2 = 3 4 . Question 4, chap 27, sect 2....
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This homework help was uploaded on 04/10/2008 for the course PHY 303L taught by Professor Turner during the Spring '08 term at University of Texas.

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hw5 solutions - homework 05 – SMITH TAYLOR – Due 4:00...

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