The resistance of a coil is $4.2\mathrm{\Omega }$ at ${100}^0\mathrm{C}$  and the temperature coefficient of resistance of its material is $0{.004}^0\mathrm{C}$ .  Its resistance at $0^0\mathrm{C}$  is

Solution:

Resistance $R_2=4.2\mathrm{\Omega }$ Temperature $t_2={100}^{\circ }\mathrm{c}$ Temperature ${\mathrm{t}}_1=0^{\circ }\mathrm{c}$
Temperature of coefficient  $\mathrm{\alpha }=0{.004}^0\mathrm{C}$ 
$\alpha =\frac{R_2-R_1}{R_1(t_2-t_1)}\Rightarrow 4\times {10}^{-3}=\frac{4.2-R_1}{R_1\times 100}$

$\Rightarrow 0.4R_1+R_1=4.2\Rightarrow 1.4R_1=4.2\therefore R_1=3\mathrm{\Omega }$