# 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) $500^{\circ}C$

N neha
V Vakul

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 = 200 $\Omega$

$\alpha$ = 0.005$^{\circ}$ C-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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