p33_084 - 84. (a) Using XC = 1/ωC and VC = IC XC , we...

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Unformatted text preview: 84. (a) Using XC = 1/ωC and VC = IC XC , we find ω= IC = 5.77 × 105 rad/s . CVC This value is used in the subsequent parts. The period is T = 2π/ω = 1.09 × 10−5 s. (b) Adapting Eq. 26-22 to the notation of this chapter, UE,max = 1 CV 2 = 4.5 × 10−9 J . 2C (c) The discussion in §33-4 shows that UE,max = UB,max . (d) We return to Eq. 31-37 (though other, equivalent, approaches could be explored): −EL di = dt L By the loop rule, EL is at its most negative value when the capacitor voltage is at its most positive (VC ). Using this plus the frequency relationship between L and C (Eq. 33-4) leads to di dt (e) Differentiating Eq. 31-51, we have dUB di = Li . dt dt As in the previous part, we use L = 1/ω 2 C . We also use a simple sinusoidal form for the current, i = I sin ωt: dUB 1 = 2 I 2 ω sin ωt cos ωt dt ωC where this I is equivalent to the IC used in part (a). Using a well-known trig identity, we obtain dU B dt = max = ω 2 CVC = 998 A/s . max I2 I2 (sin 2ωt)max = 2C 2ω 2ω 2 C which yields a (maximum) time rate of change (for UB ) equal to 2.60 × 10−3 J/s. ...
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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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