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AP EAMCET2014PhysicsCurrent Electricity

Wires A and B have resistivities _A and _B , ( _B=2 _A ) and have lengths l_A and l_B . If the diameter of the wire B is twice that of A and the two wires have same resistance, then l_B l_A is

Options

  1. A2
  2. B1
  3. C1 2
  4. D1 4

Correct answer

A. 2

Step-by-step solution

The given, _B=2 _A, R_A=R_B=R Let, r_A=r r_B=2 r According to formula, aligned R_A & = _A I_A r_A^2 R_B & = _B I_B r_B^2 R_A & =R_B _A I_A r_A^2 & = _B I_B r_B^2 aligned aligned I_B I_A & = r_B^2 r_A^2 _A _B & = (2 r)^2 r^2 _A 2 _B & = 4 r^2 r^2 _A 2 _A & = 4 2 =2 aligned

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