The resistance of a wire at 20 degree celsius and 100 degree celsius i

1.	The resistance of a wire at 20 degree celsius and 100 degree celsius is 3 ohm-m and 4 ohm-m respectively. The resitivity of the wire at 0 degree celsius is?
Answer» answer : OPTION (1) 11/4 ohm.m explanation : relation between resistivity and temperature is given by, $\rho=\rho_0[1+\alpha\Delta(T-T_0)]$ where $\rho$ is resistivity at temperature T, $\rho_0$ is resistivity at temperature $T_0$ and $\alpha$ is COEFFICIENT of temperature. Let $\rho_0$ is initial resistivity at 0°C then, at 20°C , $\rho=3\Omega.m$ $3=\rho_0[1+\alpha(20-0)]$ ....(1) at 100°C, $\rho=4\Omega.m$ $4=\rho_0[1+\alpha(100-0)]$ ....(2) from EQUATIONS (1) and (2), 4 - 3 = 1 = $80\rho_0\alpha$ ...(3) and 3/4 = [1 + 20α]/[1 + 100α] or, 3 + 300α = 4 + 80α or, 220α = 1 or, α = 1/220 , putting it in equation (3), 1 = 80 × $\rho_0$ × 1/220 220/80 = 11/4 = $\rho_0$ hence, option (1) is correct choice.