Question

the resistance of one kg of a material in the cubical form of each side l is R. The resistance, if the same material is used as a rectangular block of length 2l is​

Answer 1

The resistance of rectangular block will be four time of cubical block.

Explanation:

1. Material is same, also amount of material is same.

2.Means resistivity($\rho$) of material is same, and also volume is same.

3. From conservation of material

 Volume of cubical block = volume of rectangle block

 $l^{3}=2l\times A$    

Where A = base area of rectangle block which is perpendicular to current flow.

So A= $\frac{l^{2}}{2}$     ...1)

4. From Resistance of material (R) = $\rho \frac{Length through in current direction}{area perpendicular to current direction}$    ...2)

5.  Resistance of cubical block

      $R_{cubical} = \rho \frac{l}{l^{2}}=\rho \frac{1}{l}$       ...3)

6.  Resistance of rectangle block

     $R_{rectangle} = \rho \frac{2l}{A}$        ...4)

7.   from equation 4) and equation 1)

    $R_{rectangle} = \rho \frac{2l}{A}=\rho \frac{4}{l}$     ...5)

8. From equation 3) and equation 5 ) it is clear that resistance of rectangle block is four times of resistance of cubical block.

     

   

Answer 2

Answer:

4R

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