Engineering: A small bulb is rated at 7.5 W when operated at 125 V. The tungsten filament has a temperature coefficient of resistivity α = 0.0045/°C. When the filament is hot and glowing, its temperature is seven times room temperature (20 °C). What is the resistance of the filament (in ohms) at room temperature?

560 inExplanation:14x8x5=560...

A small bulb is rated at 7.5 W when operated at 125

AestheticRoses

21.01.2022

The resistance of the Tungsten filament is 1352.8 Ohms

Explanation:

The temperature dependent value of resistance at any given temperature is given by the formula:

$R = R_{ref}[1+ \alpha(T-T_{ref} )]$

where

R = resistance of conductor at temperature T

R = $\frac{V^{2} }{Power} =\frac{125^{2} }{7.5} = 2083.333\Omega$

$R_{ref}$ = resistance of conductor at reference temperature (20 degrees C)

T = Temperature of conductor = $7\times 20 = 140C$

$T_{ref}$ = Reference Temperature (20C)

In the question, we are asked to find $R_{ref}$ which can be got by making it the subject of the formula as shown below:

$R_{ref} =\frac{R}{[1+ \alpha(T-T_{ref} )]}$

$R_{ref} =\frac{2083.333}{[1+0.0045(140-20 )]}= 1352.79\Omega$

∴The resistance of the filament at room temperature = 1352.8 Ohms

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