Question

At what temperature will the resistance of a copper wire become three times its value at $0^{\circ} C$ ? (temperature coefficient of resistance for copper $\left.=4 \times 10^{-3} /{ }^{\circ} C \right)$

• A. $400^{\circ} C$
• B. $450^{\circ} C$
• C. $500^{\circ} C$
• D. $550^{\circ} C$

Answer 1

Answer: (C)

From definition of temperature resistance coefficient
$R_{t} =R_{0}(1+\alpha t)$
$3 R_{0} =R_{0}\left(1+4 \times 10^{-3} t\right)$
$3=1+4 \times 10^{-3} t$
$4 \times 10^{-3} t=2$
$t= \frac{2}{4 \times 10^{-3}}$
$=500^{\circ} C$