Question: The electrical resistance \(R\) in ohms \((\Omega)\) for a pure metal wire is related to its temperature \(T\) in \({ }^{\circ} \mathrm{C}\) by the formula

in which \(R_{0}\) and \(k\) are positive constants.

1. Make a hand-drawn sketch of the graph of \(R\) versus \(T\), and explain the geometric significance of \(R_{0}\) and \(k\) for your graph.
2. In theory, the resistance \(R\) of a pure metal wire drops to zero when the temperature reaches absolute zero \(\left(T=-273^{\circ} \mathrm{C}\right)\). What information does this give you about $k ? \((c) A tungsten bulb filament has a resistance of\) 1.1 \Omega$ at a temperature of \(20^{\circ} \mathrm{C}\). What information does this give you about \(R_{0}\) for the filament?
   (d) At what temperature will the tungsten filament have a resistance of \(1.5 \Omega ?\)
   
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