Calculate the temperature at which the resistance of a conductor becomes 20% more than its resistance at 27°C. The value of the temperature coefficient of resistance of the conductor is $2.0 \times 10\frac{-4}{\text{K}}.$
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Given, $\text{R}_{27}=\text{R}(\text{say}),\text{R}_\text{T}=\text{R}+\frac{20}{100}\text{R}=1.2\text{R},\text{T}_1=27+273=300\text{K}$
From relation,
$\text{R}\text{T}=\text{R}_{27}[1+\alpha(\text{T}_2-300)]$
$\Rightarrow1.2\text{R}=\text{R}[1+2.0\times10^{-4}(\text{T}_2-300)]$
$\Rightarrow1+2.0\times10^{-4}(\text{T}_2-300)=1.2$
$\Rightarrow2.0\times10^{-4}(\text{T}_2-300)=0.2$
$\text{T}_2-300=\frac{0.2}{2.0\times10^{-4}}$
$\text{T}_2=1000+300=1300\text{K}$
From relation,
$\text{R}\text{T}=\text{R}_{27}[1+\alpha(\text{T}_2-300)]$
$\Rightarrow1.2\text{R}=\text{R}[1+2.0\times10^{-4}(\text{T}_2-300)]$
$\Rightarrow1+2.0\times10^{-4}(\text{T}_2-300)=1.2$
$\Rightarrow2.0\times10^{-4}(\text{T}_2-300)=0.2$
$\text{T}_2-300=\frac{0.2}{2.0\times10^{-4}}$
$\text{T}_2=1000+300=1300\text{K}$
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