Exam3_2004Fall

Exam3_2004Fall - Physics 8.02 TEST 3 MASHUP Fall 2004...

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Physics 8.02 TEST 3 MASHUP Fall 2004 PLEASE DETACH THIS SHEET AND USE AT YOUR CONVENIENCE Some (possibly useful) Relations: = surface closed o inside Q ε dA E outside to inside from points dA = = b a a b b to a from moving V V V ds E C Q V U = 1 2 C V 2 = Q 2 2C d A o plate parallel κ = C τ = RC V = i R P joule = i V = i 2 R = V 2 /R 2 ˆ 4 o q r µ π × = vr B 2 ˆ 4 o I r × = ds r dB F = q v × B ext ext I dF ds B τ τ = µ µ × B thru closed path dI ⋅= o Bs G G v = dA B ds E dt d ε = N d φ B dt L = N B i ε = L di dt / L R = U L = 1 2 L i 2 u B = | B | 2 2 0 T = 2 π ω = 1 f Free RLC Circuit No Damping: 0 () s in ( ) o Qt Q t ω = , 1 o LC = Driven LRC Circuit: if ε (t) = ε m sin( ω t ), then i (t) = i m sin( ω t - φ ), where i m = ε m R 2 + ω L – 1 ω C 2 1/2 and tan φ = ω L – 1 ω C R 1 LC XLX C == Integrals that may be useful a b dr b a = ) / ln( 1 a b dr r b a = = b a dr r b a 1 1 1 2 Fall 2004 Exam 3 Mashup
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Problem 1: Four Multiple Choice Questions (20 points) Circle your choice for the correct answer to the four questions given below. A : A parallel plate capacitor with area A and plate separation d is initially charged. We want to discharge it using a conductor of resistivity ρ shaped as a solid cylinder of area A and height d that fits right between the plates of the capacitor. What is the time constant τ that governs the discharge? 1. 0 2 A d ερ = 2. 2 0 d A = 3. 0 = 4. 0 ε = B. The circuit shown below contains an AC generator which provides a source of sinusoidally varying emf ( t ) = 0 sin( ω t) , a resistor with resistance R = 1 ohm, and a "black box", which contains either an inductor or a capacitor, or both . We measure the current in the circuit at an angular frequency =30 radians/sec and find that the current is exactly in phase with the driving emf at this frequency.
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Exam3_2004Fall - Physics 8.02 TEST 3 MASHUP Fall 2004...

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