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Unformatted text preview: ding to the formula L di + Ri = E , dt R > 0, L > 0, E > 0 constant. p(t ) dt . Show that
x (a) Find i if i(0) = 0. (b) What upper limit does the current approach as t → ∞? (c) In how many seconds will the current reach 90% of its limit? 40. The current i in an electrical circuit consisting of a resistance R, inductance L, and a voltage E sin ωt , varies with time according to the formula L di + Ri = E sin ωt , dt R > 0, L > 0, E > 0 constant y(x) = e−H (x)
a q(t ) eH (t ) dt 34. 35. 36. 37. is the solution of the differential equation that satisﬁes the initial condition y(a) = 0. Show that if y1 and y2 are solutions of (8.8.1), then z = y1 − y2 is a solution of the differential equation (∗) above. A thermometer is taken from a room where the temperature is 72◦ F to the outside, where the temperature is 32◦ F. After 1 minute the thermometer reads 50◦ F. What will the ther2 mometer read at t = 1 minute? How long will it take for the thermometer to read 35◦...
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This note was uploaded on 10/12/2010 for the course MATH 12345 taught by Professor Smith during the Spring '10 term at University of Houston - Downtown.
- Spring '10