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Lightbulb brightness in a circuit

  1. Feb 15, 2015 #1
    1. The problem statement, all variables and given/known data
    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

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

    3. 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.
     

    Attached Files:

  2. jcsd
  3. Feb 15, 2015 #2
    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
     
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