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  • Confused! kindly explain, A copper wire of resistance 4W is melted and redrawn to thrice its original length. Find the resistance of stretched wire.

A copper wire of resistance 4W is melted and redrawn to thrice its original length. Find the resistance of stretched wire.

  • Option 1)

    40 W

  • Option 2)

    60 W

  • Option 3)

    45 W

  • Option 4)

    36 W

 

Answers (1)

As we learnt

Stretching of wire -

If a conducting wire stretches it's length increases area of cross-section decreases but volume remains constant.

- wherein

Since volume of the wire does not change.

Þ l1A1 = l2 A2  where l­1­  and A1 are the initial length and cross-section of the wire, and l2 and A2 are the final length and cross-section.

                Þ           \frac{{{l_1}}}{{{l_2}}} = \frac{{{A_2}}}{{{A_1}}}$     . . . (1)

                                           R_1=\rho\frac{{{l_1}}}{{{A_1}}}$   and     R_2=\rho\frac{{{l_2}}}{{{A_2}}}$

                                Þ           \frac{{{R_1}}}{{{R_2}}} = \frac{{{l_1}}}{{{l_2}}} \times \frac{{{A_2}}}{{{A_1}}} = \frac{{{l_1}}}{{{l_2}}} \times \frac{{{l_1}}}{{{l_2}}}$     . . . (2)

                                Þ           \frac{{{R_1}}}{{{R_2}}} = \frac{{l_1^2}}{{l_2^2}}$             

 as l2 = 3l1

Þ R2 = 9R1   = (9 ´ 4)W = 36 W


Option 1)

40 W

Option 2)

60 W

Option 3)

45 W

Option 4)

36 W

Posted by

neha

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