Six similar bulbs are connected as shown in the figure with a DC source of emf E, and zero internal resistance.
The ratio of power consumption by the bulbs when (i) all are glowing and (ii) in the situation when two from section A and one from section B are glowing, will be :

(a) `2: 1`
(b) `4 : 9 `
(c) `9 : 4`
(d) `1 : 2 `

Options

A. `2: 1`
B. `4 : 9 `
C. `9 : 4`
D. `1 : 2 `

Answer

C

Explanation

`9 : 4 `

If equivalent resistance in case (1) is `R_(1) ` then :
`(1)/(R_(1)) = (1)/(2R) + (1)/(2R) + (1)/(2R) = (3)/(2R)`
`therefore R_(1) = (2R)/(3)`
`therefore` Electric power `P_(1) = (E^(2))/(R_(1))`
`therefore P_(1) = (E^(2))/((2R)/(3)) = (3)/(2).(E^(2))/(R)`
`therefore P_(1) = (3)/(2) P " " [ because P = (E^(2))/(R) ]`
If equivalent resistace in case (2) is `R_(2)` then :
`R_(2) = (R)/(2) + R`
= `(3R)/(2) `
`therefore` Electric power `P_(2) = (E^(2))/(R_(2)) = (E^(2))/((3R)/(2)) `
`therefore P_(2) = (2)/(3) ((E^(2))/(R) ) = (2)/(3) P `
`therefore (P_(1))/(P_(2)) = ((3)/(2) P)/((2)/(3)P) = (9)/(4) `