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Two metallic wires A and B are made using copper. The radius of wire A is r while its length is l . A dc voltage V is applied across the wire A , causing power dissipation, P . The radius of wire B is 2 r , and its length is 2 l and the same dc voltage V is applied across it causing power dissipation P₁ . Which one of the following is the correct relationship between P and P₁ ?

Options

  1. AP=2 P₁
  2. BP=P₁ / 2
  3. CP=4 P₁
  4. DP=P₁

Correct answer

B. P=P₁ / 2

Step-by-step solution

Resis tance of wire R = l ~A = l r ^2 If R₀ is resistance of first wire, the resistance of second wire. aligned & R = 2 l (2 r )^2 = 1 2 l r ^2 = R ₀ 2 & R = V ^2 R ₀ and P ₁= V ^2 R _ 0 / 2 =2 P aligned

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