If `X, Y` and `Z` in figure are identical lamps, which of the following changes to the brightness of the lamps occur when switch `S` is closed?

Options

A. X stays the same, Y decreases
B. X increases, Y decreases
C. X increases, Y stays the same
D. X decreases, Y increases

Explanation

The “brightness” that a bulb shows is related to the power consumed by it.
Since the bulbs are identical, let the resistance of each of them be R and let the EMF of the battery be E
When the switch S is open, current through X and Y `E/(2R)` is and current through Z is zero
Power consumed by X (and power consumed by Y), , `P_x=P_y=(E/(2R))^2 R=E^2/(4R)`
Now, if the switch S is closed, net resistance of the circuit is `(3R)/2`
So, current through X is `(2E)/(3R)` and current through both Y and Z is `E/(3R)`.
Therefore, power consumed by X `P_x=((2E)/(3R))^3 R=(4E^2)/(9R)`
And, power consumed by each of Y and Z `P_Y=P_z=(E/(3R))^2 R=E^2/(9R)`
So, when the switch is closed, the brightness of X increases and the brightness of Y decreases.