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COMEDK202510 May 2025Morning ShiftPhysicsCurrent ElectricityActual

The resistance of a wire is 5 ohm at 25^ C and 7 ohm at 100^ C . The resistance of the wire at 0^ C is

Options

  1. A0.1 ohm
  2. B2 3 ohm
  3. C5 3 ohm
  4. D13 3 ohm

Correct answer

D. 13 3 ohm

Step-by-step solution

The resistance of a wire at temperature t is given by the formula R_t = R₀(1 + t) , where R₀ is the resistance at 0^ C and is the temperature coefficient of resistance. Given R₂₅ = 5 , at 25^ C and R₁₀₀ = 7 , at 100^ C , we have the following equations: 5 = R₀(1 + 25 ) (1) 7 = R₀(1 + 100 ) (2) Dividing equation (2) by equation (1): 7 5 = 1 + 100 1 + 25 7(1 + 25 ) = 5(1 + 100 ) 7 + 175 = 5 + 500 2 = 325 = 2 325 Substituting back into equation (1): 5 = R₀(1 + 25 2 325 ) 5 = R₀(1 + 50 325 ) = R₀(1 + 2 13 ) 5 = R₀( 15

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