1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

AC, 2 appliances in parallel, one of them is disconnected

  1. May 12, 2017 #1
    1. The problem statement, all variables and given/known data
    Question1.png
    A light bulb (L1) and a cooker (R1) are connected to the same wire. The wire consists
    of two copper conductors with a cross section of 1.5 mm2 and a length of 22.3 m.
    When SW1 is closed the heating element of the cooker will be turned on. It has a
    power dissipation of 2300 W when it is supplied with 230 V. The light bulb has a
    power dissipation of 23 W when it is supplied with 230 V.
    As shown on the diagram the wire will from the beginning be supplied with 230 V.
    a) What is the voltage drop across light bulb L1 when the cooker is turned off, ie. the
    switch SW1 is open?
    b) What is the voltage drop across the light bulb L1 when the cooker is turned on, ie.
    the switch SW1 is closed?
    c) What is the power dissipated by light bulb L1 when the cooker is turned off?
    d) What is the power dissipated by light bulb L1 when the cooker is turned on?
    Note:
    The light bulb and the heating element can be considered to be constant ohmic
    resistances.
    Specific resistance of copper


    3. The attempt at a solution
    attsol.png
    + on paper P=I^2*R and I=V/R --> R=V^2/P
    Assumptions:
    • Voltage in parallel doesn't change
    • Current coming through the wire splits into the branches


    I've been stuck for the last two hours.

    I can find out the resistance of the wire, but not the p.d. it produces, since I don't know the current (which is dependent upon how much Voltage is left after the first wire has been passed). Not even voltage division works, since the Resistance of the two appliances is dependent upon the current passing through them and that current is once again, dependent on just how much Voltage remains after the first wire...

    Learning to use mathematica for physics:
    Problem would produce recursion, since variables were interdependent - R_L and R_R on DV_W, which is dependent on R_Total (which is, wait, dependent on R values of the appliances, which depend on the current, which depends on the voltage left after the first wire............


    I'm lost, (in a recursive loop, just like tho Mathematica), please help. Need another perspective...

    Edit: Now that I'm cooking lunch and thinking about it, V isn't limited to the given value V_rms, (V_max*sqrt(2)/2), so the the appliances could draw the P/V current...
     
    Last edited: May 12, 2017
  2. jcsd
  3. May 12, 2017 #2

    cnh1995

    User Avatar
    Homework Helper

    That's not correct.

    What can you say about the resistances of the cooker and the bulb? Can you find them from their ratings?

    (Also, as per PF rules, you should avoid using bold font in the OP since it is considered yelling.)
     
  4. May 12, 2017 #3
    Can you explain why it is not correct? As I said, I'm kind of lost.

    P/V = I
    R=V/I
    R=V^2/P

    But doesn't this assume, that all of the 230Vrms gets to the cooker and the bulb? Or the rating is independent of the actual Voltage, that gets to them?

    Formatting got copied from the sub-title...
     
  5. May 12, 2017 #4

    gneill

    User Avatar

    Staff: Mentor

    Yes, the ratings are based on the condition that the device is supplied at its rated voltage. For this reason you can find an equivalent resistance for the devices under the given assumption that they can be considered to be constant ohmic resistances.
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?
Draft saved Draft deleted