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This question contains Statement-1 and Statement-2. Of the four choices given after the statements, choose the one that best describes the two statements.

Statement-1: The temperature dependence of resistance is usually given as R=R_{0}(1+\alpha \Delta t). The resistance of a wire changes from 100\, \Omega \; to\; 150\, \Omega when its temperature is increased from 27^{\circ}C\; to\; 227^{\circ}C. This implies that \alpha =2.5\times 10^{-3}/^{\circ}C.

Statement-2:  R=R_{0}(1+\alpha \Delta t)   is valid only when the change in the temperature \Delta T is small and \Delta R=(R-R_{0})< < R_{0} .

 

  • Option 1)

    Statement-1 is true, Statement-2 is false

  • Option 2)

    Statement-1 is true, Statement-2 is true; Statement-2 is the correct explanation of Statement-1.

  • Option 3)

      Statement-1 is true, Statement-2 is true; Statement-2 is not the correct explanation of Statement-1.

  • Option 4)

    Statement-1 is false, Statement-2 is true

 

Answers (2)

best_answer

 

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

 

 From the statement given \alpha = 2.5X 10^{-3}/^{\circ}C

The resistance of wire change from 100°\Omega to 150\Omega when the temperature is increased from 27°c to 227°c

It is true that \alpha is small but (150 -100)\Omega or 50 \Omega is not very much less than 100 \Omega .

i.e. R-R^{\circ} cc R^{\circ}  is not true.

 


Option 1)

Statement-1 is true, Statement-2 is false

Option 2)

Statement-1 is true, Statement-2 is true; Statement-2 is the correct explanation of Statement-1.

Option 3)

  Statement-1 is true, Statement-2 is true; Statement-2 is not the correct explanation of Statement-1.

Option 4)

Statement-1 is false, Statement-2 is true

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