Question

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?

Answer 1

The resistance of the Tungsten filament is 1352.8 Ohms

Step-by-step 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 =
`(V^(2) )/(Power) =(125^(2) )/(7.5) = 2083.333\Omega`

`R_(ref)` = resistance of conductor at reference temperature (20 degrees C)

T = Temperature of conductor =
`7* 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) =(R)/([1+ \alpha(T-T_(ref) )])`

`R_(ref) =(2083.333)/([1+0.0045(140-20 )])= 1352.79\Omega`

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