Figure ( a ) shows a rod of resistive material. The resistance per unit length o

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 = 4.93x 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 5.2 V battery (figure (c)). You want the current in the length to transfer energy to thermal energy at the rate of 186 W. At what position x = L should you cut the rod?
(in m)

Explanation / Answer

Solution :-

P = V^2/R

R = (5.2)^2/186 = 0.145 ohm

integral 4.93x dx from 0 to L = 0.145 ohm

4.93*L^2/2 = 0.145

L = 0.58m

Related Questions

Navigate

• Browse (All)
• Browse F
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.