The resistance of a wire at room temperature 20^ C is found to be 10 . If resistance of the wire increases by 10 % , then the temperature of the wire will be (The temperature coefficient of the material of the wire at 0^ C is 0.002/^ C )

Step-by-step solution

R₁ = 10 at T₁ = 20°C , R₂ = 11 (10% increase), ₀ = 0.002/°C Using R_T = R₀(1 + ₀ T) : R₂ R₁ = 1 + ₀ T₂ 1 + ₀ T₁ 11 10 = 1 + 0.002 T₂ 1 + 0.002 20 = 1 + 0.002 T₂ 1.04 1.1 1.04 = 1 + 0.002 T₂ 1.144 = 1 + 0.002 T₂ T₂ = 0.144 0.002 = 72°C