HW10solutions-10

# HW10solutions-10 - Physics 2213 Homework 10 Solutions...

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Physics 2213 Homework 10 Solutions Spring 2010 Q30.2 [Transformer] Transformers work because of Faraday's Law of magnetic induction — a changing magnetic flux produces an induced emf. Since the areas and orientations of the transformer's coils are fixed, a changing magnetic field is required to produce a changing magnetic flux, which requires a changing electric current. The induced emf 2 = -N 2 (d B /dt) in the secondary coil is nonzero as long as the electric current i 1 in the primary coil is changing. A DC (constant) current won't produce a changing magnetic flux, so a transformer won't work with DC. An AC current is needed since it is always changing. 30.9 [Inductor] (a) 3 (0.260 H)(0.0180 A/s) 4.68 10 V L di dt (b) V a >V b so that the induced current flows through the circuit in the same direction as the original current. The inductor acts like a battery with its + terminal at a to oppose the change in current. 30.10. [Inductor] (a) Given that that V a > V b , the induced current must be in the same direction as the given current. This means that the induced current is opposing a decrease in the given current. Therefore, the given current must be decreasing with time. (b) dt di L V ab , so s A H V L V ab / 00 . 4 260 . 0 04 . 1 , which is decreasing and constant. Then t i , or ) ( i f i f t t i i , and A s s A A i f . 4 ) 0 . 2 ( / . 4 0 . 12 . 30.60. [LR Circuit] For this RL circuit, the current is given by Eq.(30.14): ( / ) ( ) (1 ) R L t i t e R . (a) The voltage behaves the same as the current. Since R V is proportional to i , the scope must be across the 150 resistor. (b) From the graph, as , 25 V, R tV so there is no voltage drop across the inductor, so its internal resistance must be zero. / max ) tr R V V e . When t , max max 1 1 0.63 . R V V V e From the graph, max 0.63 16 V VV at 0.5 ms t . Therefore 0.5 ms . / 0.5 ms LR gives (0.5 ms) (150 ) 0.075 H L . (c) At all times 25.0 V RL . At 0 t all the battery voltage appears across the inductor since 0 i . At t all the battery voltage is across the resistance, since /0 di dt . The graph of v vs. t if the scope is connected across the coil is sketched below. 0.0 0.5 1.0 1.5 2.0 2.5 0 5 10 15 20 25 V L (Volts) t (ms)

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Physics 213 Homework 10 30.43. [2 Solenoids] Let’s call the outer solenoid solenoid #1. The mutual inductance of two solenoids is derived in Example 30.1. For the two solenoids in this problem 0 1 2 , AN N M l where A
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## This note was uploaded on 06/08/2010 for the course PHYS 213 taught by Professor Perelstein during the Spring '08 term at Cornell University (Engineering School).

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HW10solutions-10 - Physics 2213 Homework 10 Solutions...

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