Question

The Resistance of a conductor is $X\Omega$ at $0^{o}C$ temp. Find the temperature at which the resistance of conducter becomes $3x\Omega$.The temp. Certificate of resistance for conductor is $0.4\times {10}^{-2}o{C}^{-1}$ which is constant

Answer 1

Formula
$R_2=R_2[1+\alpha (T_2-T_1\left)\right]$
$R_1\to Resistanceat{T}_1$
$R_2\to Resistanceat{T}_2$
$\alpha \to temperaturecoefficient$
$R_1=x$
$R_2=3x$
$T_1=0^o$
$T_2=?$
$\alpha =0.4\times {10}^{-2}$
$3x=x(1+0.4\times {10}^{-2}(T_2-0\left)\right)$
$3=1+0.4\times {10}^{-2}\left(T_2\right)$
$2=0.4\times {10}^{-2}{T}_2$
$T_2=\frac{2}{0.4\times {10}^{-}2}=\frac{2\times {10}^3}{4}={500}^{o}C$