The resistance of a wire is 5 ohm at 50°C and 6 ohm at 100°C. The resistance of the wire at 0°C will be

  • Option 1)

    3\: \: ohm

  • Option 2)

    2\: \: ohm

  • Option 3)

    1\: \: ohm

  • Option 4)

    4\: \: ohm

 

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

 

 

Given :R_{50}=5\Omega ,R_{100}=6\Omega

R_{t}=R_{0}\left ( 1+\alpha t \right )

Where     R_{t} = resistance of a wire at t^{\circ}C

R_{0}= resistance of a wire at 0^{\circ}C,\alpha = Temperature coefficient of resistance.

\therefore R_{50}= R_{0}\left [ 1+\alpha 50 \right ]

R_{100}= R_{0}\left [ 1+\alpha 100 \right ]

or\: \: \: \: R_{50}- R_{0}= R_{0}\alpha \left ( 50 \right )\cdots \cdots \cdots \cdots \left ( i \right )

or\: \: \: \: R_{100}- R_{0}= R_{0}\alpha \left ( 100 \right )\cdots \cdots \cdots \cdots \left (ii \right )

Divide (i) by (ii), we get

\frac{5-R_{0}}{6-R_{0}}= \frac{1}{2}

or 10-2R_{0}= 6-R_{0}

or\: \: \: \: R_{0}=4\Omega

 


Option 1)

3\: \: ohm

This option is incorrect.

Option 2)

2\: \: ohm

This option is incorrect.

Option 3)

1\: \: ohm

This option is incorrect.

Option 4)

4\: \: ohm

This option is correct

N neha

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