The resistance of a device component decreases as the current through it increases and it is described by the relation, `R=(0.2I)/(I-4)`, where I is the current. Determined the minimum power deliver. (Assume, `Igt4`)

Options

A. 22.4 W
B. 18.6 W
C. 19. 8 W
D. 21. 6W

Answer

D

Explanation

Given resistance R of a device decreases as cuurent, I increases by the relation,
`R=(0.2l)/(l-4)`
`:.` Power of the electric device, `P=I^(2)R`
`=I^(2).(0.2I)/(I-4)" ".......(i)`
Power will be minimum, if
`(dP)/(dI)=0`
`(d)/(dI)((0.2I^(3))/(I-4))=0`
`((I-4)xx0.2xx3l^(2)-0.2I^(3))/((I-4)^(2))=0`
`0.6I^(3)-2.4I^(2)-0.2I^(3)=0`
`0.4I^(2)(I-6)=0" "("":'Igt4)`
`impliesI-6=0`
`I=6A`
From Eq. (i) minimum power
`P_(InIn)=(0.2xx6^(3))/(6-4)=(43.2)/(2)=21.6 W`
Hence, the minimum power delivered in device 21.6 W.