1.

A uniform wire of resistance 100ohms is melted & recast into a wire of half length & double cross sectional area that of the original.What would be the resistance of new wire formed?

Answer»

The VOLUME of the wire REMAINS same when it is recast.
       A₂ = 2 *A₁       and           L₂ = L₁ / 2          
 
 RESISTANCE R = ρ * L / A
      R₂ = ρ L₂ / A₂ = ρ L₁ / (2 2 A₁)  = R₁ / 4   = 100 Ω / 4 = 25 Ω

  HENCE resistance becomes 1/4 th.
 
You can also SAY that, resistance is proportional to the length and inversely proportional to the area of cross section.  Hence, the resistance becomes 1/2 * 1/2 times initial.



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