In the circuit diagram, heat produces in R, 2 R and 1.5 R are in the ratio of

Options

A. `4 : 2 : 3`
B. `8 : 4 : 27`
C. `2 : 4 : 3`
D. `27 : 8 : 4`

Answer

B

Explanation

Current in resistance R is
`I_(1) = (12R)/(R+2R) = (2)/(3)I`
Heat produced in resistance R in time t is
`H_(1) = I_(1)^(2) Rt = ((2)/(3) I)^(2) Rt`
Current in resistance 2R is
`I_(2) = (IR)/(2R+R) = (1)/(3)I`
Heat produced in resistance 2R in same time t is
`H_(2) = I_(2)^(2) 2Rt = ((1)/(3)I)^(2) 2Rt`
Current in resistance 1.5R is
`I_(3) =I`
Heat produced in resistance 1.5R in same time t is
`H_(3) = I_(3)^(2) (1.5R) t= l^(2)(1.5R) t`
`:. H_(1) : H_(2) : H_(3) = ((2)/(3)I)^(2) Rt: ((1)/(3)I)^(2) 2Rt: I^(2) (1.5R)`
`= (4)/(9) : (2)/(9): (3)/(2)= 8: 4 : 27`