Question

how much would you have to raised the temperature of a copper wire ( originally at 20 ° C ) to increased its resistanced by 20 %

Answer 1

How much would you have to raised the temperature of a copper wire (originally at $T_{\text{ref}} = 20{}^{\circ}\text{C}$) to increased its resistance by $20\%$?

**Solution.**

A temperature coefficient of resistance $\alpha$ is given by:

$$\alpha = \frac{1}{R} \frac{dR}{dT},$$

where $R$ is the conductor resistance at reference temperature, $dR$ is the increment of resistance, $dT$ is the temperature increment.

The temperature coefficient of resistance of copper is $\alpha = 4 \cdot 10^{-3} \, \text{J/°C}$. So we have:

$$dT = \frac{dR}{R\alpha} = \frac{20\%}{4 \cdot 10^{-3} \, \text{J/°C}} = 50{}^{\circ}\text{C}.$$

The final temperature is $T = T_{\text{ref}} + dT = 20{}^{\circ}\text{C} + 50{}^{\circ}\text{C} = 70{}^{\circ}\text{C}$.

**Answer:** $dT = 50{}^{\circ}\text{C}; T = 70{}^{\circ}\text{C}$.