• # question_answer The resistance of a wire at 300 K is found to be$0.3$ $\Omega$. If the temperature coefficient of resistance of wire is $1.5\times {{10}^{-3}}{{K}^{-1}}$, the temperature at which the resistance becomes $0.5\,\Omega$. is A)  720 K                           B)  345 K C)  993 K                           D)  690 K

Given ${{R}_{300}}\,=0.3\,\Omega ,\,\,{{R}_{\tau }}\,=0.6\,\Omega$ $T=300\,K={{27}^{o}}C$ Temperature coefficient of resistance $\alpha =1.5\,\times {{10}^{-3}}\,{{K}^{-1}}$ ${{R}_{300}}\,={{R}_{0}}(1+\alpha \times 27)$ (where ${{R}_{0}}$ is resistance at $0{}^\circ C$ or $273{}^\circ K$.) $0.3={{R}_{0}}(1+1.5\,\times {{10}^{-3}}\,\times 27)$            ?(i) Again ${{R}_{t}}={{R}_{0}}\,(1+\alpha t)$ $0.6={{R}_{0}}(1+{{10}^{-3}}\times t)\,$                  ?(ii) Dividing eq. (ii) by eq(i) we get $\frac{0.6}{0.3}=\frac{1+1.5\times {{10}^{-3}}t}{1+1.5\,\times {{10}^{-3}}\,\times 27}$ $2(1+1.5\times {{10}^{-3}}\,\times 27\,)\,=1+2.5\,\times {{10}^{-3}}t$ $t=\frac{1.081}{1.5\,\times {{10}^{-3}}}\,={{720}^{0}}\,C\,=993K$