The resistance of a wire is 5 Ω at 50 ° C and 6 Ω at 100 ° C . The resistance of the wire at 0 ° C will be

Step-by-step solution

Given: R 50 = 5   Ω ,   R 100 = 6   Ω R t = R 0 1 + α t Where R t = resistance of a wire at t   ° C , R 0 = resistance of a wire at 0   ° C , α   = temperature coefficient of resistance. ∴    R 5 0 = R 0 1 + α 5 0 and R 1 0 0 = R 0 1 + α 1 0 0 or R 5 0 - R 0 = R 0 α 5 0 R 1 0 0 - R 0 = R 0 α 1 0 0   Dividing (i) by (ii), we get 5 - R 0 6 - R 0 = 1 2 or 10 - 2 R 0 = 6 - R 0 or R 0 = 4   Ω