A fuse wire with radius 1 mm blows at `1.5` amp . The radius of the fuse wire of the same material to blow at 3 A will be

Options

A. `4^(1//3)` ohm
B. `3^(1/4)` ohm
C. `2^(1/2)` ohm
D. `3^(1//2)` ohm

Answer

A

Explanation

Fuse law-
`I prop r^(3//2) rArr r_(2)/r_(1) = (i_(2)/i_(1))^(2/3) = (3/1.5)^(2//3) = (4)^(1/3)`
`rArr r_(2) = 4^(1/3) xx r_(1) = 4^(1/3) mm`