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HW10solutions - Physics 213 Q30.2 Homework 10 Solutions...

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Physics 213 Homework 10 Solutions Spring 2008 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 ² 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 chanign magnetic flux, so a transformer won't work with DC. An AC current is needed since it is always changing. 30.9 [Inductor] I DENTIFY and S ET U P : Apply ± = L di / dt . Apply Lenz’s law to determine the direction of the induced emf in the coil: The induced emf is directed so as to oppose the decrease in the current. E XECUTE : (a) ± = L ( di / dt ) = (0.260 H)(0.0180 A/s) = 4.68 ² 10 ³ 3 V (b) Terminal a is at a higher potential since the coil pushes current through from b to a and if replaced by a battery it would have the + terminal at a . 30.10. [Inductor] I DENTIFY : Apply ± = ² L di dt . S ET U P : The induced emf points from low potential to high potential across the inductor. E XECUTE : (a) The induced emf points from b to a , in the direction of the current. Therefore, the current is decreasing and the induced emf is directed to oppose this decrease. (b) ± = L ² i / ² t , so ± i / ± t = V ab / L = (1.04 V) / (0.260 H) = 4.00 A/s.
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