Explanation:
Here \({R_{20}} = 20\Omega ,\,{R_{500}} = 60\Omega ,\,{R_1} = 25\Omega \)
As temperature changes are large we take
\({T_i} = 0\) & \({T_f} = T\)
\(R = {R_0}\left( {1 + \alpha T} \right)\)
Where \(\alpha \) is the temperature coefficient of resistance
\( \Rightarrow 20 = {R_0}(1 + \alpha \times 20)\,\,\,\,\,\,\,\,\,\,\,\,(1)\)
\( \Rightarrow 60 = {R_0}(1 + \alpha \times 500)\,\,\,\,\,\,\,\,\,(2)\)
Divide (2) by (1), we get
\( \Rightarrow \alpha = \frac{2}{{440}} = \frac{1}{{220}}\,^\circ {C^{ - 1}}\)
Again
\( \Rightarrow 20 = {R_0}\left( {1 + \frac{1}{{220}} \times 20} \right)\,\,\,\,(3)\)
\( \Rightarrow 25 = {R_0}\left( {1 + \frac{1}{{220}} \times T} \right)\,\,\,\,\,\,(4)\)
Dividing (4) by (3), we get
\(\frac{{25}}{{20}} = \frac{{\left( {1 + \frac{1}{{220}} \times T} \right)}}{{\left( {1 + \frac{1}{{220}} \times 20} \right)}} \Rightarrow T = 80^\circ C\)
