Chapter 4, Problem 4.2P

The temperature dependence of resistance is also quantified by the relation $R_2=R_1\left[1+\alpha \left(T_2-T_1\right)\right]$

where $R_1$ and $R_2$ are the resistances at temperatures $T_1$ and $T_2,$ respectively, and $\alpha$ is known as the temperature coefficient of resistance. If a copper wire has a resistance of $55\Omega$ at $20°\text{C,}$ find the maximum permissible operating temperature of the wire if its resistance is to increase by at most $20\%.$ Take the temperature coefficient at $20°\text{C}$ to be $\alpha =\mathrm{0.00382.}$