The three resistance of equal value are arranged in the different combination shown below. Arrange them in increasing order of power dissipation.
(I) (II)
(IV)

Options

A. `I lt III lt II lt IV`
B. `II lt III lt IV lt I`
C. `III lt II lt IV lt I`
D. `I lt IV lt III lt II`

Answer

D

Explanation

For circuit (1), effective resistance = 3 R
For circuit (2), effective resistance `= R//3`
For circuit (3), effective resistance
`=(Rxx2R)/(R+2R)=(2)/(3) R`
For circuit (4), effective resistance `=(R )/(2)+R=(3)/(2)R`
Thus `3R gt (3)/(2)R gt (2)/(3) R gt (R )/(3)`
`therefore P=(V^(2))/(R ) therefore P prop (1)/(R )`
`therefore P_(2) gt P_(3) gt P_(4) gt P_(1) or P_(1) lt P_(4) lt P_(3) lt P_(2)`
(in increasing order) or `I lt IV lt III lt II`