Figure ( a ) shows a rod of resistive material. The resistance per unit length o
ID: 1779852 • Letter: F
Question
Figure (a) 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 = 4.80x dx, where dR is in ohms and x is in meters. Figure (b) 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 5.5 V battery (figure (c)). You want the current in the length to transfer energy to thermal energy at the rate of 197 W. At what position x = L should you cut the rod?
m
Explanation / Answer
rate of thermal energy P = E^2/R
resistance R = P*E^2 = 197*5.5^2 = 5959.25 ohms
resistance R= integration dR
R = integration(4.8x dx ) from x = 0 to x = L )
5959.25 = 4.8*x^2/2 from x = 0 to x = L )
5959.25 = 2.4*L^2
L = 49.8 m <<<-----ANSWER
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