Walker, Halliday & Resnick — Current and Resistance: Problem 40

40 Figure 26-25a shows a rod of resistive material. The resistance per unit length of the rod increases in the positive direction of the x axis. At any position x along the rod, the resistance dR of a narrow (differential) section of width dx is given by dR = 5.00x dx, where dR is in ohms and x is in meters. Figure 26-25b shows such a narrow section. You are to slice off a length of the rod between x = 0 and some position x = L and then connect that length to a battery with potential difference V = 8.0 V (Fig. 26-25c). You want the current in the length to transfer energy to thermal energy at the rate of 180 W. At what position x = L should you cut the rod?