First slide

Thermometry

Question

The resistance of a bulb filament is 100 $Ω$ at a temperature of 100°C. If its temperature coefficient of resistance be 0 .005/°C, its resistance will become 200 $Ω$ at a temperature of

Moderate

A

300°C
B

400°C
C

500°C
D

200°C

Solution

We know that
$R_{t} = R_{0} [1 + αΔT]$
Here $100 = R_{0} [1 + 0 \cdot 005 \times 100]$ ………..(1)
and $200 = R_{0} [1 + 0 \cdot 005 \times T]$ …………….(2)
where T is the temperature in °C at which the resistance becomes 200 $Ω$
Dividing eq. (2) by eq. [1), we get
$\frac{200}{100} = \frac{1 + 0 \cdot 005 T}{1 + 0 \cdot 005 \times 100}$
Solving, we get, T = 400°C

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