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Exercise:
The temperature of the tungsten filament in a lightbulb can be estimated from the lightbulb’s resistance at room temperature TrO and in operation. At room temperature the resistance of a VO/PO light bulb is measured to be RrO. Asing a linear relation between resistance and temperature calculate the filament temperature when the light bulb is on. Is the real value lower or higher?

Solution:
When the light bulb is on its resistance is given by R fracDelta VI fracDelta VfracPDelta V fracDelta V^P It follows for the temperature coefficient alpha_ fracDelta RR_ Delta T fracR-R_R_ Delta T fracfracDelta V^P-R_R_ Delta T fracDelta V^ - P R_P R_ Delta T Solving for the temperature increase yields Delta T fracDelta V^-R_PP R_ alpha_ The filament temperatre in operation is then T T_ + Delta T TF Tr + fracV^-P times RrP times Rr times al T approx resultTS The real value is lower because the resistivity increases more than the linear tr i.e. it reaches the operational temperature at a lower temperature than predicted by the linear model.
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Exercise:
The temperature of the tungsten filament in a lightbulb can be estimated from the lightbulb’s resistance at room temperature TrO and in operation. At room temperature the resistance of a VO/PO light bulb is measured to be RrO. Asing a linear relation between resistance and temperature calculate the filament temperature when the light bulb is on. Is the real value lower or higher?

Solution:
When the light bulb is on its resistance is given by R fracDelta VI fracDelta VfracPDelta V fracDelta V^P It follows for the temperature coefficient alpha_ fracDelta RR_ Delta T fracR-R_R_ Delta T fracfracDelta V^P-R_R_ Delta T fracDelta V^ - P R_P R_ Delta T Solving for the temperature increase yields Delta T fracDelta V^-R_PP R_ alpha_ The filament temperatre in operation is then T T_ + Delta T TF Tr + fracV^-P times RrP times Rr times al T approx resultTS The real value is lower because the resistivity increases more than the linear tr i.e. it reaches the operational temperature at a lower temperature than predicted by the linear model.
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Branches
Electrodynamics
Tags
light bulb, resistance, temperature
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Difficulty
(2, default)
Points
0 (default)
Language
ENG (English)
Type
Calculative / Quantity
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Decoration
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Link