An 11.0-W energy-efficient fluorescent lightbulb is designed to produce the same

Question

An 11.0-W energy-efficient fluorescent lightbulb is designed to produce the same illumination as a conventional 40.0-W incandescent lightbulb. Assuming a cost of $0.120/kWh for energy from the electric company, how much money does the user of the energy-efficient bulb save during 120 h of use? A coil of Nichrome wire is 32.0 m long- The wire has a diameter of 0.430 mm and is at 20.0 degree C. If it carries a current of 0.560 A, what is the magnitude of the electric field in the wire? If it carries a current of 0.560 A, what is the power delivered to it? If the temperature is increased to 400 degree C and the potential difference across the wire remains constant, what is the power delivered?

Explanation / Answer

Q10.

length=32 m

diameter=0.43 mm=43*10^(-5) m

radius=diameter/2=21.5*10^(-5) m

resistivity of nichrome=10^(-6)

then resistance of the wire=resistivity*length/area

=10^(-6)*32/(pi*radius^2)

=32*10^(-6)/(pi*(21.5*10^(-5))^2)=220.36 ohms

part a:

current=0.56 A

resistance=220.36 ohms

then potential difference=current*resistance=123.4 volts

then electric field=potential difference/radius=5.7395*10^5 N/C

part b:

current=0.56 A

power =current^2*resistance

=0.56^2*220.36=69.105 W

part c:

temperature coefficient of resistivty of ncihrome=0.0004

so resistance at 400 degree celcius=220.36*(1+0.0004*(400-20))=253.85 ohms

then power delivered=potential difference^2/resistance

=123.4^2/253.85=59.986 W

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