Review. When a straight wire is warmed, its resistance is given by $R=R_{0}\left[1+\alpha\left(T-T_{0}\right)\right]$ according to Equation $27.19,$ where $\alpha$ is the temperature coefficient of resistivity. This expression needs to be modified if we include the change in dimensions of the wire due to thermal expansion. Find a more precise expression for the resistance, one that includes the effects of changes in the dimensions of the wire when it is warmed. Your final expression should be in terms of $R_{0}, T, T_{0},$ the temperature coefficient of resistivity $\alpha,$ and the coefficient of linear expansion $\alpha^{\prime} .$
