Answer:
The change in temperature is [tex]\Delta T = 1795 K[/tex]
Explanation:
From the question we are told that
The temperature coefficient is [tex]\alpha = 4 * 10^{-3 }\ k^{-1 }[/tex]
The resistance of the filament is mathematically represented as
[tex]R = R_o [1 + \alpha \Delta T][/tex]
Where [tex]R_o[/tex] is the initial resistance
Making the change in temperature the subject of the formula
[tex]\Delta T = \frac{1}{\alpha } [\frac{R}{R_o} - 1 ][/tex]
Now from ohm law
[tex]I = \frac{V}{R}[/tex]
This implies that current varies inversely with current so
[tex]\frac{R}{R_o} = \frac{I_o}{I}[/tex]
Substituting this we have
[tex]\Delta T = \frac{1}{\alpha } [\frac{I_o}{I} - 1 ][/tex]
From the question we are told that
[tex]I = \frac{I_o}{8}[/tex]
Substituting this we have
[tex]\Delta T = \frac{1}{\alpha } [\frac{I_o}{\frac{I_o}{8} } - 1 ][/tex]
=> [tex]\Delta T = \frac{1}{3.9 * 10^{-3}} (8 -1 )[/tex]
[tex]\Delta T = 1795 K[/tex]
