Lightbulb brightness in a circuit

[phunphysics]

Homework Statement

The circuit has identical light bulbs. A fourth identical light bulb is added to the circuit. How does the brightness of the original light bulbs change?

a)All of them get dimmer
b)X,Z get dimmer, Y brighter
c)X,Z brighter, Y dimmer
d)X,Y dimmer, Z brighter
e)X,Y brighter, Z dimmer

Homework Equations

$P=I^2R$
$R_{eq} = R_1 + R_2 (series)$
$\frac{1}{R_{eq}} = \frac{1}{R_1} + \frac{1}{R_2} (parallel)$

The Attempt at a Solution

If I treat the light bulbs as identical resistors, then the equivalent resistance of the setup is R/3 since they are all parallel. If the fourth is added, then the equivalent resistance changes and I calculated that it becomes 2R/5, which means that more current will be drawn from the battery. If that's the case, I thought that X and Z would get brighter and Y would be dimmer, so c) would be my answer.

 

[throneoo]

I think you got the original equivalent resistance wrong. You should calculate the equil. resistance of Y and Z first using the formula for parallel resistors and add it to X in series.

after that you could think about the effect of the additional resistor on the voltage distribution of X and the branches