A fuse wire of radius 0.2 mm blows off with a current of 5 a . The fuse wire of same material but of radius 0.3 mm will blow off with a current of

Options

A. `(15)/(2)A`
B. `(5sqrt(3))/(2)` A
C. `(5sqrt(3))/(2)`A
D. `5sqrt((27)/(8))A`

Answer

C

Explanation

If I = current rating of fuse wire and r = radius of fuse wire then relation `I^(2) prop r^(3)`
`(I_(2))/(I_(1)) = (r_(2)/(r_(1)))^(3//2)` given `r_(1)= 0.2 "mm" I_(1)= 5A`
`r_(2)= 0.3 mm I_(2)= ?`
`I_(2)= 5xx((0.3)/(0.2))^(3//2) = 5sqrt((27)/(8))A `