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 = 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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