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The resistance of a bulb filament is $100\Omega$ at a temperature of 100ºC. If its temperature coefficient of resistance be 0.005 per ºC its resistance will become $200\Omega$ at a temperature of

Option 1)
$200^{\circ}C$

Option 2)
$300^{\circ}C$

Option 3)
$400^{\circ}C$

Option 4)
$500^{\circ}C$

Answers (2)

As we learnt in

Temperature co-efficient of Resistivity -

$\alpha=\frac{R_{T}-R_{o}}{R_{o}(T-T_{o})}$

- wherein

Where the value of $\alpha$ is different at different temperatures

R₁₀₀=100 $\Omega$

R_t = 200 $\Omega$

$\alpha$ = 0.005C^-1

$100= R_{0}\left [ 1+0.005\times 100 \right ]\cdots \cdots \cdots \cdots (i)$

$R_{t}= R_{0}\left [ 1+0.005t \right ]$

$200= R_{0}\left [ 1+0.005\times 100 \right ]\cdots \cdots \cdots \cdots (ii)$

$\therefore from \ R_{eq} (i) and (ii)$

$\frac{100}{200}= \frac{\left [ 1+0.005\times 100\right ]}{\left [ 1+0.005t \right ]}$

$1+0.005t=2+1$

$or\: \: \: t=400^{\circ}C$

Option 1)

$200^{\circ}C$

This is incorrect.

Option 2)

$300^{\circ}C$

This is incorrect.

Option 3)

$400^{\circ}C$

This is correct.

Option 4)

$500^{\circ}C$

This is incorrect.

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Vakul

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