Exam3_2007Fall_Solution

Exam3_2007Fall_Solution - Physics 8.02 Exam Three Solutions...

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Physics 8.02 Exam Three Solutions Fall 2007 Please Remove this Tear Sheet from Your Exam Some (possibly useful) Relations: 2 1 ˆ 4 o dq d r πε = Er G free, inside closedsurface o Q d κ ε ⋅= ∫∫ EA G G w points from inside to outside d A G total d d dt dt Φ = Ed s BdA G GG G v moving from to b ab b a a VV V Δ= = Es G G d 2 ˆ 4 o q c r μ π × =< < vr Bv G G G 2 ˆ 4 o I d d r × = sr B G G ˆ where points source observer rf r o mt o 0 closed surface d BA G G w through 0 contour E o d dI dt με Φ ⎛⎞ + ⎜⎟ ⎝⎠ Bs G G v where I through is the current flowing through any open surface bounded by the contour: through open surface I d =⋅ JA G G d s is right-handed with respect to d A 2 2 0 1 22 EB o B uE u == () ext q =+ × FE v B GGG G ext d Fs B G G G 2 cent. Fm v = r IA = μ n G ± τ μ B G z zz dB F dz = VI R L R A ρ = 2 2 V PI V I R ohmic heating R Δ =Δ = = Q C V = Δ parallelplate o A C d = 2 2 1 2 2 Q UC V C = R 1 C CX C = = τ ω B,self,total back dI LL Φ I dt 2 1 2 L UL I = / L LR X L = = 2 2 tan LC ZR X RX X XR ϕ = Series RLC: 2 fT k ω =π=π =πλ 1 2 00 cT f k =λ =ω = με 0l i g h t 0 ˆˆ ˆ Ev B ×= EB p = absorb reflect 0 12 ; SS PP cc = = μ SE B G G G Dt If the function satisfies the equation t dt dD =− / t o De , then = ˆˆ ˆˆˆˆ 0 Cross-products of unit vectors: ×=×= × = ii jjkk ˆ k ˆ × = i j × = ki ˆ j × = j Some potentially useful numbers 2 97 2 0 1N m T m 91 0 4 1 0 4C eo k μπ × = × Breakdown of air E ~ 3 x 10 6 V/m .5 Gauss ed) 00 nm l - A Earth’s B Field B ~ 5 x 10 -5 T = 0 Speed of light c = 3 x 10 8 m/s Light (blue to r λ = 400 nm to 7 Electron charge e = 1.6 x 10 -19 C Avogadro’s num N A = 6.02 x 10 23 mo ber
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MIT PHYSICS DEPARTMENT p. 2 of 10 Problem 1: Five Short Questions. Fill in the blanks with the correct answer Each problem is worth 4 points for the correct answer, 2 points for a partially correct answer (at our discretion). If you don’t know the answer you can earn 1 point for admitting that by leaving it unanswered and writing “I don’t know” (make this clear!). Question A (4 points out of 20 points): A circuit consists of a battery with emf V , an inductor with inductance L , a capacitor with capacitance C , and three resistors, two with resistance R , one with 2 R as shown in the sketch. The switch has been closed a very long time. At time t = 0 the switch is opened. Immediately afterwards, which of the following statements about currents is true? 123 1) 2) 33 4) 5) 6) 22 2 7) None of the above VV RR V iii R == = After a long time C is “full” and L acts as wire, so i 1 = i 3 = V/3R . When switch is opened the inductor will keep i 3 the same. i 1 will go to zero and i 2 = - i 3 . Question B (4 points out of 20 points): What kind of a filter is the circuit below, if the input is at left and the output at right? 1) High Pass C R 2) Low Pass 3) Band Pass 4) Stop Band 5) Notch Filter At low frequencies C has a high reactance and hence will see a large voltage drop. At high frequencies is will look like a wire (small voltage drop). So this is a low pass filter.
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MIT PHYSICS DEPARTMENT p. 3 of 10
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Exam3_2007Fall_Solution - Physics 8.02 Exam Three Solutions...

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