Question
(a) To what temperature must you raise a resistor made of constantan to double its resistance, assuming a constant temperature coefficient of resistivity? (b) To cut it in half? (c) What is unreasonable about these results? (d) Which assumptions are unreasonable, or which premises are inconsistent?

a) $500000\textrm{C}^\circ$

b) $-250000\textrm{C}^\circ$

c) The sun's surface is about $6000^\circ\textrm{C}$, therefore a $500000\textrm{C}^\circ$ temperature rise is not reasonable. Constantan would change phase.

Absolute zero is $-273^\circ\textrm{C}$, so a $250000\textrm{C}^\circ$ temp decrease would require starting at a temperature so high that Constantan would be a plasma.

d) Assuming the termperature coefficient of resistivity is constant with changes in temperature is a false assumption.

Solution Video