Assuming all bulbs are identical, rank the brightness of the bulbs, from brightest to dimmest.

Options

A. `A gt D = H gt B = C gt E = F = G`
B. `A gt B = C gt D = H gt E = F = G`
C. `A gt D = H gt E = F = G gt B = C`
D. all have equal brightness

Answer

A

Explanation

(a) For the branch containing `A, B` and `C`.
`R_(eq) = (3 R)/(2)`
Current in `A : I_(1) = (E )/(R_(eq)) = (2 E)/(3R)`
Current in each of `B` and `C : I'_(1) = (I_(2))/(2) = (E)/(3R)`
For the branch containing `D, E, F, G` and `H` :
`R_(eq) = (7 R)/(3)`
Current through `D` and `H`:
Current through each of `E, F` and `G`:
`I'_(2) = (I_(2))/(3) = (E)/(7 R)` Since `I_(1) gt I_(2) gt I'_(1) gt I'_(2)`
`A gt D = H gt B = C gt E = F = G`