P28_053 - ) e t/ into V R = iR to obtain V R = q R e t/ =...

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53. (a) The initial energy stored in a capacitor is given by U C = q 2 0 2 C , where C is the capacitance and q 0 is the initial charge on one plate. Thus q 0 = p 2 CU C = p 2(1 . 0 × 10 6 F)(0 . 50 J) = 1 . 0 × 10 3 C . (b) The charge as a function of time is given by q = q 0 e t/τ ,where τ is the capacitive time constant. The current is the derivative of the charge i = dq dt = q 0 τ e t/τ , and the initial current is i 0 = q 0 . The time constant is τ = RC =(1 . 0 × 10 6 F)(1 . 0 × 10 6 Ω) = 1 . 0s. Thus i 0 =(1 . 0 × 10 3 C) / (1 . 0s)=1 . 0 × 10 3 A. (c) We substitute q = q 0 e t/τ into V C = q/C to obtain V C = q 0 C e t/τ = µ 1 . 0 × 10 3 C 1 . 0 × 10 6 F e t/ 1 . 0s =(1 . 0 × 10 3 V) e 1 . 0 t , where t is measured in seconds. We substitute i =( q 0
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Unformatted text preview: ) e t/ into V R = iR to obtain V R = q R e t/ = (1 . 10 3 C)(1 . 10 6 ) 1 . 0 s e t/ 1 . 0 s = (1 . 10 3 V) e 1 . t , where t is measured in seconds. (d) We substitute i = ( q / ) e t/ into P = i 2 R to obtain P = q 2 R 2 e 2 t/ = (1 . 10 3 C) 2 (1 . 10 6 ) (1 . 0 s) 2 e 2 t/ 1 . 0 s = (1 . 0 W) e 2 . t , where t is again measured in seconds....
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This note was uploaded on 11/12/2011 for the course PHYS 2001 taught by Professor Sprunger during the Fall '08 term at LSU.

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