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History Bookmarks Window Help Pearson eText Pearson eText tance Used 2013 Hon... a session 0-85695822 omework.H Problem 26.84 Problem 26.84 Part A Some light-dimmer switches use a variable resistor as shown in the figure. The slide moves from position to 1, and the resistance up to slide position z is proportional to (the total resistance is Rw-150 at What is the power expended in the lighttub it z 1.00 Express your answer using two significant figures. My Answers Give Up Incorrect; Try Again; 4 attempts remaining Part B What is the power expended in the ightbubif a -0657 Express your answer using two significant figures of 1 Rvar= 150 P. 120V My Answers Cive = 240 Part C expended in the 8

Explanation / Answer

given resistance at slide position x is proportional to x

so R(x) = kx

now, R(x) at x = 1 is 150 ohm

so 150 = k*1

k = 150 ohm/m

R(x) = 150x

A. from the circuit

Rx and Rbulb are in parallel

so, Req = Rx*Rbulb(Rx + Rbulb)

Rbulb = 240 ohm

and at x = 1, R(x) = 150 ohm

Req = 150*240/(150 + 240) = 92.307 ohm

so potential drop across Rbulb = V = 120 V

Power dissipated = V^2/Rbulb = 120^2/240 = 60 W

B. AT X = 0.65

R(x) = 0.65*150 = 97.5 ohm

Req = 97.5*240/(97.5 + 240) = 69.33 ohm

also, 150 - R(x) and Req are in series

so current from the battery be i

using V = iR

120 = i(150 - 97.5 + 69.33)

i = 0.984 A

Voltage drop in 150 - R(x) = i(150 - 97.5) = 51.709 V

so VOltage droip across bulb = 120 - 51.709 = 68.29 V

so power dissipated by bulb = V^2/Rbulb = 68.29^2/240 = 19.431 W

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