Suppose a light bulb (R = 2.88 k?) is connected in series with an inductor (L =

Question

Suppose a light bulb (R = 2.88 k?) is connected in series with an inductor (L = 14.4 H) and a large DC voltage supply (Vb = 240. V). (Assume that the solenoid and battery both have zero internal resistance.) The switch is closed at time t = 0

B) Find the value of the power dissipated by the light bulb after a very long period of time (as t ->infinity)?

C) Find a mathematical expression for the power dissipated by the light bulb as a function of time. Show your work. You may express your final answer EITHER in terms of numerical quantities OR in terms of R. L. & Vb. Express your final answer in simplest form.

Explanation / Answer

B. time constant of RL ckt is T = L/R = 14.4/2880 = 5 milli secs

current in the curcuit is i = V/R = 240/2880 = 0.08334 Amps

power dissiopated P = Vi = 240 * 0.08334

P = 20.0016 Watts

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C. equation for Rise of current in RL ckt is given By I = Io((1-e^-t/T)------1

where T is Time constant

also Power = Vi

so multilping eqn 1 by V on both sides

P = P0( 1-e^-t/T)    or P = P0(1-e^-Rt/L)

where p = Vi

and P0 = VbI0

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extending furthur,

initail power = V^2/R = 240*240/2880 = 20 Watts

power after 1 time constnt is P = 20 *(1-e^-1)

P = 20*(1-1/e)

P = 0.637 *20

P = 12.74 Watts after 1 time constant

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