Question

A wire of given material having length l and area of cross section A has a resistance of 4ohm. What would be the resistance of another wire of the same material having length l/2 and area of cross section 2A???

Answer 1

Resistance = p l/a [ p is constant]
For first wire length = l and area of croos section = a
Resistance = p l/a = 4 ohm [given]

For second wire length = l/2 and area of cross section = 2a
Resistance = p (l/2) / 2a
                   = p l/4a
                   = p l/a * 1/4 [p l/a = 4 ohm]
                   = 4*1/4 =  1 ohm

The resistance of second wire = 1 ohm

Answer 2

Hey..!!!

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l = l

A = A

R1 = 4 ohm

R1 = rho  × l/ A

i . e 4 = rho × l / A

in the another wire

l = i/2 × l

A = 2A

R = (rho × 1/2 l) / 2A

  =( rho × l/A ) × 1 / 4

we have rho l / A = 4 ohm

so, 4 × i/ 4

 = 1 ohm Ans.

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I Hope It's help you...!!!!