Power through parallel resistors.

Discussion in 'Homework Help' started by Pulsed, Sep 13, 2012.

  1. Pulsed

    Thread Starter Member

    Sep 10, 2012
    41
    3
    This one confuses me. You have three resistors, 2 4r and one 6r, each with a power limit of 1 Watt. If they are all put in parallel so that they form a composite resistor, what is the max wattage that the composite resistor can handle before it burns up?
    I thought 3W but am clearly wrong. I also got this explanation, which did not help me.

    "Because 3W on the three resistors in // means 2.12V across each resistor (U=PR−−−−√) and then U^2/R=(2.12V)^2/4ohm=1.124W for the 4ohm resistors. It is higher than 1W and can not be correct. Don't forget than we do not have three equals resistors."

    Many thanks for your kind responses!
     
  2. #12

    Expert

    Nov 30, 2010
    16,336
    6,820
    With all resistors in parallel, they must all have the same voltage. The lowest resistance will have the highest current, and so, the highest wattage for any voltage applied to all three. That will find the highest voltage allowed. Then you can calculate the power disipated in each resistor.
     
  3. Pulsed

    Thread Starter Member

    Sep 10, 2012
    41
    3
    Thanks 12, but I would appreciate if someone could show me how you would approach this practically?
     
  4. justtrying

    Active Member

    Mar 9, 2011
    329
    351
    can I ask how you came up with 3W? And does the question ask for max wattage, because you cannot exceed the rating and they are already rated for 1W.
     
  5. Pulsed

    Thread Starter Member

    Sep 10, 2012
    41
    3
    Certainly, the original question was: Given that each individual resistor can dissipate up to 1 watt of power before burning up, how much total power in watts ( W ) can the smallest-valued composite resistor dissipate before burning up? Answer: 3
    incorrect



    I thought 3 because, given that each resistor was rated at one watt, three in parallel would handle 3 watts. I see now that logic is flawed because the resistances are different.


    How would you go about putting this into an algebraic equation? That is where I am really stuck. Upon searching Google I have not come up with this seemingly simple answer.
     
  6. bertus

    Administrator

    Apr 5, 2008
    15,648
    2,348
  7. justtrying

    Active Member

    Mar 9, 2011
    329
    351
    To be honest this question is throwing me off:

    you know that the rating is 1W and the resistors are in parallel, so you can calculate maximum voltage that the resistors can handle before the rating is exceeded. To do that, as #12 said already, lowest resistance = highest current, therefore that will give you the highest voltage allowed.

    the problem I have with the question, is that all values are based on finding the maximum allowable voltage (from using 1W value) so the answers end up being 1W or less, i.e. just the rating. I am either missing something or this is a very poor question.
     
  8. JoeJester

    AAC Fanatic!

    Apr 26, 2005
    3,373
    1,159
    The lowest valued resistor "sets" the maximum voltage you can have on the parallel circuit.

    Find the voltage for 1W on the lowest resistance.

    The question asked for the total power .... so now that you computed the maximum voltage on the circuit, just compute the power for the remaining resistors. The correct answer will be 1W + next resistors power + next resistors power.

    Use Bertus' diagram.
     
    Last edited: Sep 13, 2012
    justtrying likes this.
  9. justtrying

    Active Member

    Mar 9, 2011
    329
    351
    Thanks Joe, I see now that "composite" means total. First time I see this. Makes sense now.
     
    Last edited: Sep 13, 2012
  10. bertus

    Administrator

    Apr 5, 2008
    15,648
    2,348
    Hello,

    @ justtrying,
    Now you have given the answer, without having the OP showing us his try.

    Bertus
     
  11. JoeJester

    AAC Fanatic!

    Apr 26, 2005
    3,373
    1,159
    justtrying ...

    One must be careful in the homework section when posting. We prefer not to give the answer, but to make the OP understand where they went astray so they can have the same "ah ha" moment you did.
     
  12. justtrying

    Active Member

    Mar 9, 2011
    329
    351
    Yes, my apologies to Pulsed. I've never done this before. I am sure the OP will post his work. I've fixed my reply. I don't know why I slipped.
     
  13. JoeJester

    AAC Fanatic!

    Apr 26, 2005
    3,373
    1,159
    It happens ...
     
  14. Pulsed

    Thread Starter Member

    Sep 10, 2012
    41
    3
    I am not given a voltage, or a current with which I can calculate the power, which is the part I do not understand. With just the 1w rating and the fact there are three resistors, one of which is a different value.
     
  15. bertus

    Administrator

    Apr 5, 2008
    15,648
    2,348
    Hello,

    I have given you an hint how to calculate the voltage:
    You can calculate the voltage using P = U*U/R.
    You will need to convert the formula to get the voltage.

    Bertus
     
  16. JoeJester

    AAC Fanatic!

    Apr 26, 2005
    3,373
    1,159
    If you are given a 1 W resistor of 4 ohms ... what is the maximum voltage you can apply to it without blowing it up?

    a. Do you know how to find the voltage when given the power and the resistance?
    b. Can you convert the formula that Bertus has given you?
     
  17. Pulsed

    Thread Starter Member

    Sep 10, 2012
    41
    3
    So...

    The composite resistance of 4 ohm, 4 ohm and 6 ohm values in parallel is equal to 1.5 ohms. Now you just convert the subject of the formula for power to V.

    P=(V^2)/R, P*R=V^2, SQRT(P*R)=SQRT(V^2), V=SQRT(P*R)

    Substituting values: V=SQRT(P?*1.5), V=?.

    I'm just coming stuck.
     
  18. bertus

    Administrator

    Apr 5, 2008
    15,648
    2,348
    Hello,

    What would happen if you calculate the voltage using ONE 4 Ohms resistor?
    There is given that the resistors may dissipate 1 Watt.

    Bertus
     
  19. Pulsed

    Thread Starter Member

    Sep 10, 2012
    41
    3
    It would equal SQRT(1*4). You would have a maximum of 2 volts before the resistor burned up.
     
  20. mlog

    Member

    Feb 11, 2012
    276
    36
    Based on 2 volts, what is the power dissipated by each individual resistor, and what is the total (i.e. the sum) of those powers?
     
Loading...