p33_019 - 19. (a) The charge (as a function of time) is...

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19. (a) The charge (as a function of time) is given by q = Q sin ωt ,where Q is the maximum charge on the capacitor and ω is the angular frequency of oscillation. A sine function was chosen so that q =0 at time t = 0. The current (as a function of time) is i = dq dt = ωQ cos ωt , and at t =0,itis I = ωQ .S ince ω =1 / LC , Q = I LC =(2 . 00 A) p (3 . 00 × 10 3 H)(2 . 70 × 10 6 F) = 1 . 80 × 10 4 C . (b) The energy stored in the capacitor is given by U E = q 2 2 C = Q 2 sin 2 ωt 2 C and its rate of change is dU E dt = Q 2 ω sin ωt cos ωt C . We use the trigonometric identity cos ωt sin ωt = 1 2 sin(2 ωt ) to write this as dU E dt = ωQ 2 2 C sin(2 ωt ) . The greatest rate of change occurs when sin(2 ωt )=1or2 ωt = π/ 2 rad. This means t = π 4 ω = πT 4(2 π ) = T 8
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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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