The current through a conductor is ' a ' when the temperature is 0^ C . It is ' b ' when the temperature is 100^ C . The current through the conductor at 220^ C is

Step-by-step solution

The resistance of a conductor at temperature T is given by R_T = R₀(1 + T) , where R₀ is the resistance at 0^ C and is the temperature coefficient of resistance. Given the current I = V R , where V is the constant applied voltage, we have I_T = V R₀(1 + T) = I₀ 1 + T . At T = 0^ C , I₀ = a . Thus, I_T = a 1 + T . At T = 100^ C , I = b . Substituting this into the equation: b = a 1 + 100 1 + 100 = a b 100 = a b - 1 = a - b b = a - b 100b . We need the current at T = 220^ C . Let this be I₂₂₀ . I₂₂₀ = a 1 + 220 = a 1