Answer
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Hint:We are given with nichrome wire; its resistance is given at one temperature and also value at a given voltage. We are also given a temperature coefficient of resistance. So, we can use Ohm’s law and the formula of resistance variation with temperature to arrive at our solution.
Complete step by step answer:
Ohm’s law says, \[V=IR\].
So, at some particular temperature, the resistance variation is given as \[{{R}_{t}}={{R}_{0}}[1+\alpha (T-{{T}_{0}})]\].
\[{{R}_{t}}\] is the temperature at a given temperature and \[{{R}_{0}}\] is the resistance at room temperature.
\[\alpha \]is the temperature coefficient of resistance and T is the given temperature and \[{{T}_{0}}\]is the room temperature.
Using ohm's law, \[R=\dfrac{V}{I}=\dfrac{230}{2.68}=85.82\Omega \].
Now using the second relationship,
\[\begin{align}
&\Rightarrow {{R}_{T}}={{R}_{0}}[1+\alpha (T-{{T}_{0}})] \\
&\Rightarrow 85.82=75.3[1+1.7\times {{10}^{-4}}(T-27)] \\
&\Rightarrow \dfrac{85.82}{75.3}=1+1.7\times {{10}^{-4}}(T-27) \\
&\Rightarrow 1.13=1+1.7\times {{10}^{-4}}(T-27) \\
&\Rightarrow 0.13=1.7\times {{10}^{-4}}(T-27) \\
&\Rightarrow \dfrac{0.13}{1.7\times {{10}^{-4}}}=(T-27) \\
&\therefore T=848.81{}^\circ C \\
\end{align}\]
So, the value of the steady temperature of the nichrome element is \[848.81{}^\circ C\].
Note: We have to be careful while doing the calculations and need to rake all decimal values and not just up to one place. . A positive value of the temperature of coefficient resistance of a material means that its resistance increases with an increase in temperature.Most conductive materials change specific resistance with temperature changes. That is why we have temperature variation of resistance and resistivity.
Complete step by step answer:
Ohm’s law says, \[V=IR\].
So, at some particular temperature, the resistance variation is given as \[{{R}_{t}}={{R}_{0}}[1+\alpha (T-{{T}_{0}})]\].
\[{{R}_{t}}\] is the temperature at a given temperature and \[{{R}_{0}}\] is the resistance at room temperature.
\[\alpha \]is the temperature coefficient of resistance and T is the given temperature and \[{{T}_{0}}\]is the room temperature.
Using ohm's law, \[R=\dfrac{V}{I}=\dfrac{230}{2.68}=85.82\Omega \].
Now using the second relationship,
\[\begin{align}
&\Rightarrow {{R}_{T}}={{R}_{0}}[1+\alpha (T-{{T}_{0}})] \\
&\Rightarrow 85.82=75.3[1+1.7\times {{10}^{-4}}(T-27)] \\
&\Rightarrow \dfrac{85.82}{75.3}=1+1.7\times {{10}^{-4}}(T-27) \\
&\Rightarrow 1.13=1+1.7\times {{10}^{-4}}(T-27) \\
&\Rightarrow 0.13=1.7\times {{10}^{-4}}(T-27) \\
&\Rightarrow \dfrac{0.13}{1.7\times {{10}^{-4}}}=(T-27) \\
&\therefore T=848.81{}^\circ C \\
\end{align}\]
So, the value of the steady temperature of the nichrome element is \[848.81{}^\circ C\].
Note: We have to be careful while doing the calculations and need to rake all decimal values and not just up to one place. . A positive value of the temperature of coefficient resistance of a material means that its resistance increases with an increase in temperature.Most conductive materials change specific resistance with temperature changes. That is why we have temperature variation of resistance and resistivity.
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