HW4 - Version One Homework 4 Savrasov 39819 Apr 24, 2006 1...

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Unformatted text preview: Version One Homework 4 Savrasov 39819 Apr 24, 2006 1 This print-out should have 9 questions. Multiple-choice questions may continue on the next column or page find all choices before answering. The due time is Central time. Cylindrical Capacitor 03 26:01, calculus, numeric, > 1 min, normal. 001 (part 1 of 2) 1 points A 50 m length of coaxial cable has a solid cylindrical wire inner conductor with a diam- eter of 2 . 58 mm and carries a charge of 8 . 1 C. The surrounding conductor is a cylindrical shell and has an inner diameter of 7 . 27 mm and a charge of- 8 . 1 C. Assume the region between the conductors is air. The Coulomb constant is 8 . 98755 10 9 N m 2 / C 2 . What is the capacitance of this cable? Correct answer: 2 . 68505 nF. Explanation: Let : k e = 8 . 98755 10 9 N m 2 / C 2 , Q = 8 . 1 C , = 50 m , a = 2 . 58 mm , and b = 7 . 27 mm . The charge per unit length is Q . V =- Z b a ~ E d~s =- 2 k e Z b a dr r =- 2 k e Q ln b a . The capacitance of a cylindrical capacitor is given by C Q V = 2 k e 1 ln b a = 50 m 2 (8 . 98755 10 9 N m 2 / C 2 ) 1 ln 7 . 27 mm 2 . 58 mm 1 10 9 nF 1 F = 2 . 68505 nF 002 (part 2 of 2) 1 points What is the potential difference between the two conductors? Correct answer: 3 . 0167 kV. Explanation: Therefore V = Q C = 8 . 1 C 2 . 68505 nF 1 10 9 nF 1 F 1 C 1 10 6 C 1 kV 1000 V = 3 . 0167 kV Plate Separation 26:02, calculus, numeric, > 1 min, normal. 003 (part 1 of 1) 2 points A parallel-plate capacitor has a plate area of 12 cm 2 and a capacitance of 7 pF. The permittivity of a vacuum is 8 . 85419 10- 12 C 2 / N m 2 . What is the plate separation? Correct answer: 0 . 00151786 m. Explanation: Let : A = 12 cm 2 = 0 . 0012 m 2 , C = 7 pF = 7 10- 12 F , and = 8 . 85419 10- 12 C 2 / N m 2 . C = A d d = A C = ( 8 . 85419 10- 12 C 2 / N m 2 ) 7 10- 12 F ( . 0012 m 2 ) = . 00151786 m . Version One Homework 4 Savrasov 39819 Apr 24, 2006 2 Capacitors in Parallel 26:03, calculus, numeric, > 1 min, normal....
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HW4 - Version One Homework 4 Savrasov 39819 Apr 24, 2006 1...

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