A metal wire has a resistance of 10.00 $\Omega$ at a temperature of 20.0°C. If the same wire has a resistance of 10.55 $\Omega$ at 90°C, what is the resistance when its temperature is 0.0°C?
A) 13.8 $\Omega$
B) 9.69 $\Omega$
C) 9.84 $\Omega$
D) 0.70 $\Omega$

Question

Quizplus · Accepted Answer

The resistance of a metal wire increases with increasing temperature. The temperature coefficient of resistance is given by:$$\alpha = \frac{R_2 - R_1}{R_1(T_2 - T_1)}$$where $R_1$ and $R_2$ are the resistances at temperatures $T_1$ and $T_2$, respectively.In this problem, we have:$R_1 = 10.00 \Omega$$R_2 = 10.55 \Omega$$T_1 = 20.0°C$$T_2 = 90°C$Substituting these values into the equation above, we get:$$\alpha = \frac{10.55 \Omega - 10.00 \Omega}{10.00 \Omega(90°C - 20°C)} = 0.0045°C^{-1}$$Now, we can use the equation:$$R_3 = R_1[1 + \alpha(T_3 - T_1)]$$to find the resistance at $T_3 = 0.0°C$.Substituting the values we know into this equation, we get:$$R_3 = 10.00 \Omega[1 + 0.0045°C^{-1}(0.0°C - 20°C)] = 9.84 \Omega$$Therefore, the correct answer is C) 9.84 \Omega.

A Metal Wire Has a Resistance of 10 Ω\OmegaΩ At a Temperature of 20

A Metal Wire Has a Resistance of 10 $\Omega$ At a Temperature of 20