Problem 22.54 A 40 W (120 V) lightbulb has a tungsten filament of thickness 0.03

Question

Problem 22.54 A 40 W (120 V) lightbulb has a tungsten filament of thickness 0.030 mm. The Part A has a tungsten filament of thickness 0.030 mm. The filament's operating temperature is 1500 C. How long is the filament? Express your answer to two significant figures and include the appropriate units. L=14.54 |m Submit My Answers Give Up Incorrect; Try Again; 2 attempts remaining Part B What is the resistance of the filament at 20 C? Express your answer to two significant figures and include the appropriate units. R Value Units

Explanation / Answer

formula for resistance is

R = rho L/A

formula which relates power and resistance is

R = V^2/P

equate above two equations

V^2/P = rho L/A

L = V^2 A/ P * rho

=V^2 * pi (D/2)^2/ rho * P

=(120)^2 * pi ( 0.03* 10^-3/2)^2 /5*10^-7 * 40 W

=0.508 m

rounding two two significant digits, L = 0.51 m

(b)

R = rho L/A

=5.6* 10^-8 ( 0.508)/ pi ( 0.03* 10^-3/2)^2

=40.26 ohm

rounding to two significant digits

R = 40 ohm

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