ch31-p092 - 92. (a) Eqs. 31-4 and 31-14 lead to Q = 1 ω =...

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Unformatted text preview: 92. (a) Eqs. 31-4 and 31-14 lead to Q = 1 ω = I LC = 1.27 × 10−6 C . (b) We choose the phase constant in Eq. 31-12 to be φ = − π / 2 , so that i0 = I in Eq. 31-15). Thus, the energy in the capacitor is UE = q 2 Q2 = (sin ωt ) 2 . 2C 2C Differentiating and using the fact that 2 sin θ cos θ = sin 2θ, we obtain dU E Q 2 = ω sin 2ωt . dt 2C We find the maximum value occurs whenever sin 2ωt = 1 , which leads (with n = odd integer) to 1 nπ nπ nπ t= = = LC = 8.31 × 10−5 s, 2.49 × 10−4 s,… . 2ω 2 4ω 4 The earliest time is t = 8.31× 10−5 s. (c) Returning to the above expression for dU E / dt with the requirement that sin 2ωt = 1 , we obtain FG dU IJ H dt K d E max I LC Q2 = ω= 2C 2C i 2 I I2 = 2 LC L = 5.44 × 10−3 J / s . C ...
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This note was uploaded on 06/03/2011 for the course PHY 2049 taught by Professor Any during the Spring '08 term at University of Florida.

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