Exam3_2003Fall_Solutions

# Exam3_2003Fall_Solutions - Physics 8.02 TEST 3 MASHUP...

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Physics 8.02 TEST 3 MASHUP SOLUTIONS Fall 2003 PLEASE DETACH THIS SHEET AND USE AT YOUR CONVENIENCE Some (possibly useful) Relations: F = 1 4 πε o q 1 q 2 r 2 E = q 4 o r 2 ˆ r observer to source from points r ˆ = 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 If the function satisfies the equation () Dt dD dt t =− , then / t o De = through o I = ds B = 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 ( ' ) Qt Q t ω = + , 1 ' 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

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8.02T Fall 2003 Exam 3 Mashup Solutions 1 Problem 1: Five Multiple Choice Questions (25 points) Circle your choice for the correct answer to the five questions below. A: The circuit below consists of three resistors and two batteries. If we apply Kirchhoff’s loop rule moving around the bottom loop clockwise , with the assumed directions of currents as indicated, which of the following equations is the correct one? 0 i i V ∆= 1. 21 13 3 0 IR ε ++ = 2. 3 0 −+ + = 3. 3 0 −+ = 4. 3 0 −− + = 5. 3 0 +− = 6. 3 0 = 7. 3 0 −− = 8. 3 0 =
8.02T Fall 2003 Exam 3 Mashup Solutions 2 B. The magnetic field at the center of a ring of radius a carrying current I is 2 o center I B a µ = . Thus we conclude that an order of magnitude estimate of the self-inductance of this ring is 1. 2 o a 2. o a CORRECT 22 2 o center o I L Ia B a a a π πµ Φ= = ± 3. / o a 4. 2 / o a C: A fully charged capacitor is inserted into the circuit below and the switch S is closed at time t = 0 . The charge on the capacitor as a function of time is q(t) > 0 , and the current in the circuit is I(t) . A student makes an assumption about the direction of current flow and writes down the following (correct) equation using Kirchhoff’s loop rule: 0 i i q VI R C =+ + = . Which of the following is true.

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## This homework help was uploaded on 04/07/2008 for the course 8 8.02 taught by Professor Hudson during the Fall '07 term at MIT.

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Exam3_2003Fall_Solutions - Physics 8.02 TEST 3 MASHUP...

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