Lec20V - Lecture 20-1 Lecture LEVITATION ABOVE A...

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Lecture 20 Lecture 20 -1 LEVITATION ABOVE A SUPERCONDUCTOR
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Lecture 20 Lecture 20 -2 ©2008 by W.H. Freeman and Company
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Lecture 20 Lecture 20 -3 Resistive Load Start by considering simple circuits with one element ( R , C , or L ) in addition to the driving emf . Pick a resistor R first. v R (t) and I(t) in phase Kirchhoff’s Loop Rule: ( ) ( ) ( ) 0, sin peak tI t R t t ε εε ω −= = () () Rp e a k vt I t R t V == = () V It t R = I peak + -- I(t)
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Lecture 20 Lecture 20 -4 Capacitive Load I(t) leads v(t) by 90 o (1/4 cycle) Loop Rule: () 0 sin peak qt t C t ε εω −= = cos peak dq t d t It C dt Ct ωε ω == = s in vt t C Power: ( )( ) , , ()() s sin 2 2 peak C peak C peak peak p tI t v t I t V t VI t = 0 av P = + --
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Lecture 20 Lecture 20 -5 Inductive Load v L (t) leads I(t) by 90 o (1/4 cycle) Kirchhoff’s Loop Rule: () 0 s in peak dI t tL dt tt ε εω −= = s Lp e a k dI t vt L t dt ω == Power: ( )( ) , , () () cos s sin 2 2 L peak L peak ea k p k p tI t v t I t V t VI t =− 0 av P = peak It t L + --
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Lecture 20 Lecture 20 -6 LC Oscillations 2 2 1 ,, 22 EB Qd Q UU L I I Cd t === No Resistance = No dissipation 2 0 2 0 0 2 11 0 dQ Q dt LC LC f ω π ⎛⎞ += = = ⎜⎟ ⎝⎠
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Lecture 20 Lecture 20 -7 More on LC Oscillations Energy stored in capacitor: 22 0 1 () cos 2 Ep e a k Ut Q t C ω = t 0 E U 0 t B U Energy stored in inductor: 2 00 1 s in 2 Bp e a k L Q t = 0 1 LC ω= where 0 1 s 2 e a k Q t C = 2 2 peak EB Q C += so sin peak dQ I Qt dt == Charge and current: 0 cos peak QQ t = Period is half that of Q(t) With R=0
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Lecture 20 Lecture 20 -8 READING QUIZ 1 Which of the following statements is incorrect? A| In an A. C. circuit an ideal resistor is a frequency independent component. B| At zero frequency the reactance of an ideal capacitor is infinite. C| At resonance in a driven series RLC circuit the circulating current has a minimum value.
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Lec20V - Lecture 20-1 Lecture LEVITATION ABOVE A...

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