The resistance of platinum wire at $0^{\circ} ext{C}$ is $2 ext{ } \Omega$ and $6.8 ext{ } \Omega$ at $80

Question

The resistance of platinum wire at $0^{\circ}	ext{C}$ is $2 	ext{ } \Omega$ and $6.8 	ext{ } \Omega$ at $80^{\circ}	ext{C}$. The temperature coefficient of resistance of the wire is

Accepted Answer

The formula for temperature dependence of resistance is $R_t = R_0(1 + \alpha \Delta t)$. Here $R_0 = 2 	ext{ } \Omega$, $R_t = 6.8 	ext{ } \Omega$, and $\Delta t = 80^{\circ}	ext{C}$. So, $6.8 = 2(1 + \alpha \cdot 80)$. Dividing by 2, $3.4 = 1 + 80\alpha$, which gives $2.4 = 80\alpha$. Thus, $\alpha = \frac{2.4}{80} = \frac{24}{800} = 0.03 = 3 	imes 10^{-2} 	ext{ }^{\circ}	ext{C}^{-1}$.

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