The resistance of a wire at 300 ~K is found to be 0.3 . If the temperature coefficient of resistance of wire is 1.5 10⁻³ ~K ⁻¹ , the temperature at which the resistance becomes 0.6 is

Step-by-step solution

Given, aligned R ₃₀₀ &=0.3 , R _ t =0.6 , T &=300 ~K =27^ C aligned Temperature coefficient of resistance, =1.5 10⁻³ ~K ⁻¹ R ₃₀₀= R ₀(1+ 27) 0.3= R ₀ (1+1.5 10⁻³ 27 ) ...(i) Again, R _ t = R ₀(1+ t ) 0.6= R ₀ (1+1.5 10⁻³ t ) ...(ii) Dividing Eq. (ii) by Eq. (i), we get 0.6 0.3 = 1+1.5 10⁻³ t 1+1.5 10⁻³ 27 2 (1+1.5 10⁻³ 27 )=1+1.5 10⁻³ t 2+81 10⁻³=1+1.5 10⁻³ t 2+0.081=1+1.5 10⁻³ t t = 1.081 1.5 10⁻³ =720^ C =993 ~K