PHY 303L-Exam3 - midterm 03 VARELA CHRISTOPHER Due 11:00 pm...

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midterm 03 – VARELA, CHRISTOPHER – Due: Nov 15 2007, 11:00 pm 1 Question 1, chap 32, sect 5. part 1 of 1 10 points In a series RLC ac circuit, the resistance is 8 Ω, the inductance is 25 mH, and the capac- itance is 24 μ F. The maximum potential is 219 V, and the angular frequency is 100 rad / s. Calculate the maximum current in the cir- cuit. Correct answer: 0 . 528674 (choice number 8). Explanation: Let : R = 8 Ω , L = 25 mH = 0 . 025 H , C = 24 μ F = 2 . 4 × 10 - 5 F , V max = 219 V , and ω = 100 rad / s . The capacitive reactance is X C = 1 ω C = 1 (100 rad / s) (2 . 4 × 10 - 5 F) = 416 . 667 Ω . The inductive reactance is X L = ω L = (100 rad / s) (0 . 025 H) =2 . 5 Ω . The maximum current is I max = V max Z = V max ± R 2 +( X L - X C ) 2 = 219 V ± (8 Ω) 2 + (2 . - 416 . 667 Ω) 2 = 0 . 528674 A . Question 2, chap 31, sect 2. part 1 of 1 10 points A coil is wrapped with 375 turns of wire on the perimeter of a circular frame (of radius 82 cm). Each turn has the same area, equal to that of the frame. A uniform magnetic ±eld is directed perpendicular to the plane of the coil. This ±eld changes at a constant rate from 26 mT to 69 mT in 50 ms. What is the magnitude of the induced E in the coil at the instant the magnetic ±eld has a magnitude of 36 mT? Correct answer: 681 . 251 (choice number 10). Explanation: Basic Concepts: E = - N d Φ B dt Φ B ² + B · d + A = B · A Solution: E = - N d Φ B dt = - NA Δ B Δ t = - N π r 2 ( B 2 - B 1 ) Δ t = - (375) π (82 cm) 2 × (69 mT) - (26 mT) 50 ms = - 681 . 251 V |E| = 681 . 251 V . Question 3, chap 33, sect 5. part 1 of 1 10 points Consider an electromagnetic wave pattern as shown in the ±gure below. E B
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midterm 03 – VARELA, CHRISTOPHER – Due: Nov 15 2007, 11:00 pm 2 The wave is 1. traveling right to left. 2. traveling left to right. correct 3. a standing wave and is stationary. Explanation: The + E vector and + B vector are not at the same point on the velocity axis. Pick an instant in time, where the E and B Felds are at the same point on the velocity axis. z v x y E B ±or instance, let us choose the point where the + E vector is along the x axis, as shown in the above Fgures. At this same instant, the + B vector is along the negative y axis (at a point with a phase di²erence of 360 from the place on the velocity ( z ) axis where the + E vector is drawn). Then + E × + B is along the negative z axis. Therefore, the electromagnetic wave is traveling left to right. Question 4, chap 31, sect 3. part 1 of 2 10 points A horizontal circular wire loop of radius 0 . 7 m lies in a plane perpendicular to a uni- form magnetic Feld pointing from above into the plane of the loop, has a magnitude of 0 . 52 T. If in 0 . 14 s the wire is reshaped from a circle into a square, but remains in the same plane, what is the magnitude of the average induced emf in the wire during this time? Correct answer: 1 . 22703 (choice number 4). Explanation: Let : r =0 . 7m , b . 52 T , and Δ t . 14 s . The average induced emf E is given by ±E² = N ± ΔΦ Δ t ² = ΔΦ Δ t since N = 1, and ΔΦ = B ( A circle - A square ) = B ( π r 2 - A square ) .
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PHY 303L-Exam3 - midterm 03 VARELA CHRISTOPHER Due 11:00 pm...

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