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Exercise:
An old toaster contains a heating wire made of iron. The wire's resistance at room tempearture is measured to be RiO. When connected to the household voltage VO the heating power is PO. Calculate the temperature of the heating wire when in operation.

Solution:
The resistance in operation can be calculated from the voltage and the power: R fracDelta VIfracDelta VfracPDelta VfracDelta V^P The increase in resistance can be expressed as fracDelta RsscR fracR-sscRsscR fracfracDelta V^P-sscRsscR fracDelta V^-sscR PsscR P &approx fracDeltarhosscrho alphaDelta T alphaT-sscT Solving for the Temperature of the hot wire we find T &approx TF Ti + fracV^-Ritimes PaltimesRitimes P T approx resultTP
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Exercise:
An old toaster contains a heating wire made of iron. The wire's resistance at room tempearture is measured to be RiO. When connected to the household voltage VO the heating power is PO. Calculate the temperature of the heating wire when in operation.

Solution:
The resistance in operation can be calculated from the voltage and the power: R fracDelta VIfracDelta VfracPDelta VfracDelta V^P The increase in resistance can be expressed as fracDelta RsscR fracR-sscRsscR fracfracDelta V^P-sscRsscR fracDelta V^-sscR PsscR P &approx fracDeltarhosscrho alphaDelta T alphaT-sscT Solving for the Temperature of the hot wire we find T &approx TF Ti + fracV^-Ritimes PaltimesRitimes P T approx resultTP
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Attributes & Decorations
Branches
Circuits
Tags
resistance, temperature coefficient of resistivity
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Difficulty
(3, default)
Points
0 (default)
Language
ENG (English)
Type
Calculative / Quantity
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