Exam3_2005Spr_Solutions

# Exam3_2005Spr_Solutions - Physics 8.02 Exam Three Mashup...

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Physics 8.02 Exam Three Mashup Solutions Spring 2005 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 () 2 2 2 11 1 22 2 CE Q UC V u C ==∆ = E o 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 μ B G GG z zz dB F dz = thru closed path dI ⋅= o Bs G G v external self dd dt dt ⎡⎤ =− + ⎣⎦ ∫∫ ∫ E ds B dA B B dA v self Li = Bd A 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 LC 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 1 m m i RL C = +− and tan φ = ω L – 1 ω C R 1 LC XLX C == 1 Quality o o L Q R CR

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MIT PHYSICS DEPARTMENT ` page 2 Problem 1: Four Short Questions. Circle your choice for the correct answer. Question A (5 points out of 20 points): A superconducting ring of radius a has zero resistance and self-inductance L . The ring sits in a constant external magnetic field which is vertical and normal to the plane of the ring. The ring carries no current before t = 0 (see figure, which is at t = 0 ). At t = 0 , external agents come along and compress the ring until its radius is a/2, half of its original value. At that point, the total magnetic flux through the ring (due both to the external magnetic field and the self magnetic field) is 1. Four times as large as the value at t = 0 2. Twice as large as the value at t = 0 3. The same as the value at 4. One half of the value at t = 0 5. One quarter of the value at t = 0 Question B (5 points out of 20 points): In the two circuits shown, all the light bulbs and batteries are identical. If A denotes the brightness of light A , and so on, then (a) C > A = B (b) C < A = B (c) C < A < B (d) C > A > B (e) C = A > B (f) C = A < B
MIT PHYSICS DEPARTMENT ` page 3 Question C (5 points out of 20 points): In the figure the solid line shows the driving voltage in an RLC circuit at a particular frequency as a function of time and the dotted line shows the resulting current in that circuit as a function of time. In this circuit, 1. The current lags the voltage and the driving frequency is above resonance. 2. The current lags the voltage and the driving frequency is below resonance. 3. The current leads the voltage and the driving frequency is above resonance. 4. Question D (5 points out of 20 points): The switch in the circuit pictured is in position a for a long time. At t = 0 the switch is moved from a to b . The current through the inductor will reach its first maximum after t = 0 in a time: 1. 2 LC π 2 . LC 3. LC . 2 LC 5. 1 4 LC

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MIT PHYSICS DEPARTMENT ` page 4 Problem 2: Back of the Envelope Calculation (5 Pts) As always, you are not given enough information to exactly determine the answer to this question. Make your best estimates for unknowns, clearly indicating what your estimates are (e.g. Radius R ~ ….) NO CREDIT will be given for simply guessing a final numerical answer from scratch. It must be properly motivated (i.e. write equations!)
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Exam3_2005Spr_Solutions - Physics 8.02 Exam Three Mashup...

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