The three resistances of equal value (R) are arranged in different combinations shown below . Arrange them in increasing order of power dissipation.

Options

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

Answer

A

Explanation

Given : Value of each resistance = R
We know that equivalent resistance of figure I = R + R + R = 3 R
Similarly equivalent resistance of
figure II . `(2RxxR)/(2R + R) = (2R)/(3)`
And equivalent resistance of figure
III = `(R xx R xx R)/((Rxx R) + (R xx R) + (R xx R))`
`=(R^(3))/(3R^(2)) = (R)/(3)`
And equivalent resistance of figure
IV = `(RxxR)/(RxxR) + R = (3R)/(2)`
We also know that power dissipa-tion in a circuit
`(P) = i^(2) R_(eq) prop R_(eq)`
Since increasing order of the equivalent resistances in the given figures is `III lt II lt IV lt I `.
`:.` Increasing order of power dissipation is `III lt II lt IV lt I ` .