Answer: A cylindrical tungsten filament 15.0 cm long with

Chapter 25, Problem 15E

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QUESTION:

Problem 15E

A cylindrical tungsten filament 15.0 cm long with a diameter of 1.00 mm is to be used in a machine for which the temperature will range from room temperature\(\left(20^{\circ} \mathrm{C}\right)\) up to \(120^{\circ} \mathrm{C}\). It will carry a current of 12.5 A at all temperatures (consult Tables 25.1 and 25.2). (a) What will be the maximum electric field in this filament, and (b) what will be its resistance with that field? (c) What will be the maximum potential drop over the full length of the filament?

Equation Transcription:

Text Transcription:

(20degC)

120degC

Questions & Answers

QUESTION:

Problem 15E

A cylindrical tungsten filament 15.0 cm long with a diameter of 1.00 mm is to be used in a machine for which the temperature will range from room temperature\(\left(20^{\circ} \mathrm{C}\right)\) up to \(120^{\circ} \mathrm{C}\). It will carry a current of 12.5 A at all temperatures (consult Tables 25.1 and 25.2). (a) What will be the maximum electric field in this filament, and (b) what will be its resistance with that field? (c) What will be the maximum potential drop over the full length of the filament?

Equation Transcription:

Text Transcription:

(20degC)

120degC

ANSWER:

Solution 15E

We shall have to first calculate the resistivity of the tungsten filament using the equation of resistivity dependence on temperature …..(1), where is the resistivity at a reference temperature,  is temperature coefficient of resistivity and  is the difference of temperature.

Given in the question,

Length of the filament

Diameter of the filament

Radius

Therefore, area of the filament

Current

Therefore, current density

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