`B_(1), B_2 and B_3` are the three identical bulbs connected to a battery of steady emf with key `K` closed. What happens to the brightness of the bulbs `B_(1)` and `B_(2)` when the key is opened?

Options

A. Brightness of the bulb `B_(1)` increases and that of `B_(2)` decreases
B. Brightness of the bulb `B_(1)` and `B_(2)` increase
C. Brightness of the bulb `B_(1)` decrease and that of `B_(2)` increase
D. Brightness of the bulbs `B_(1)` and `B_(2)`

Answer

C

Explanation

`P_(1) = i^2R, P_(2) = P_(3) = (i^2)/(4) R`
`I = V/(R+R//2) = (2V)/(3R)`
`P_(1) = (4V^2)/(9R) , P_(2)=P_(3) = (V^2)/(9R)`
`P_(1)^(') = P_(2)^(') = (V^2)/(4R) , P_(3)^(') = 0`
`P_(1)^(') lt P_(1), P_(2)^(') ? P_(2)`.