HW-15Solutions-03-03-08

HW-15Solutions-03-03-08 - Lehigh University HW-15 Solutions...

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1 Lehigh University Physics 21, Spring 2008 March 3, 2008 HW-15 Solutions 15-1. (HRW 30-64) A coil with an inductance of 2.7 H and a resistance of 8.5 is suddenly connected to an ideal battery with ε = 100 V. At 0.086 s after the connection is made, what is the rate at which (a) energy is being stored in the magnetic field, (b) thermal energy is appearing in the resistance, and (c) energy is being delivered by the battery? Solution: 64. (a) From Eq. 30-49 and Eq. 30-41, the rate at which the energy is being stored in the inductor is () 2 1 2 2 1 11 . L LL L tt t t B L dL i dU di Li L e e e e dt dt dt R R R τ ττ εε ε −− ⎛⎞ == = = ⎜⎟ ⎝⎠ Now, L = L / R = 2.0 H/10 Ω = 0.20 s and = 100 V, so the above expression yields dU B / dt = 2.4 × 10 2 W when t = 0.10 s. (b) From Eq. 26-22 and Eq. 30-41, the rate at which the resistor is generating thermal energy is Pi R R eR R e thermal = 2 2 2 2 2 2 chch . At t = 0.10 s, this yields P thermal = 1.5 × 10 2 W. (c) By energy conservation, the rate of energy being supplied to the circuit by the battery is PP dU dt B
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HW-15Solutions-03-03-08 - Lehigh University HW-15 Solutions...

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