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 thexaxis. At any positionxalong the rod, the resistancedRof a narrow (differential) section of widthdxis given bydR= 5.05x dx, wheredRis in ohms andxis in meters. Figure (b) shows such a narrow section. You are to slice off a length of the rod betweenx= 0 and some positionx=Land then connect that length to a battery with potential differenceV= 7.9 V (Figure (c) below). You want the current in the length to transfer energy to thermal energy at the rate of 215 W. At what positionx=Lshould you cut the rod?

Explanation / Answer

Given that resistance r =5ohms VoltageV = 5 volts
PowerP = 200 watts
As we know that Power P = Voltage V * Current I Thecurrent (I)flowing through the rod will be
I= 200 watts/ 5 volts
= 40amps
Theresistance (R)of the rod will be
R = V / I
= 5 volts / 40 amps
=0.125 ohms
The resistance of 1meter rod is 5ohms
for0.125 ohms ofresitance the rod length must be 2.5 cm



change values do some alebra may be it helpful

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