Finding Voltage Source's Contribution to Power Delivered in a Circuit (Superposition)

Discussion in 'Homework Help' started by ElectronicGuru, Oct 4, 2014.

  1. ElectronicGuru

    Thread Starter New Member

    Sep 26, 2014
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    Here's the (simplified) circuit for which I have to find the power delivered by the 7 V voltage source:
    Screen Shot 2014-10-04 at 4.34.03 PM.png

    What I was doing was first finding the current in the circuit by combining the two voltage sources and then dividing by the 3.75 Ω resistance. From this, I used the power (supplied) equation:

    Power delivered by 7 V source = ((7 v + 2.25 V) / 3.75 Ω) * (7 V) = 17.27 W.

    However, the solution uses superposition to calculate the 7 V source's contribution to the power delivered:
    Screen Shot 2014-10-04 at 4.34.10 PM.png

    This seems wrong to me because I thought superposition could only be used for calculating linear responses, as stated in my textbook:
    So is the solution correct and, if so, what is my error with relation to the quote from my textbook?
     
  2. t_n_k

    AAC Fanatic!

    Mar 6, 2009
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    You are correct. The solution is incorrect.
     
  3. ElectronicGuru

    Thread Starter New Member

    Sep 26, 2014
    22
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    Do you know this for sure or are you basing it off what my textbook said? Just checking to be sure.
     
  4. crutschow

    Expert

    Mar 14, 2008
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    3,244
    I know your first solution is correct so that means the second "solution" is not. The reason is that power is proportional to V squared so you have to take both voltages into account at the same time to calculate power. Thus 7^2 plus 2.25^2 is not equal to 9.25^2.
     
  5. studiot

    AAC Fanatic!

    Nov 9, 2007
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    You should not be using superposition for the power calculation, you book is quite correct.
    This is due the the fact that a square (voltage or current ) is non linear.

    You should, howevr note that the two batteries are in series so their voltages add.

    So the total voltage applied to the resistor is (7 + 2.25) = 9.25 volts.

    Ohms law provides the current I = 9.25/3.75 = 2.47 amps

    Power is the product of current and voltage = VI

    Now do the exercise of calculating The VI for each battery individually and adding them up and then comparing this with the power obtained by multiplying the total voltage by the current.

    You might be suprised.
     
  6. ElectronicGuru

    Thread Starter New Member

    Sep 26, 2014
    22
    1
    Good tyo get confirmation. Thanks! The example you provide is actually the same one in my textbook and the reason I thought the solution was wrong.
     
  7. studiot

    AAC Fanatic!

    Nov 9, 2007
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    If you wish to consider this further

    The reason V^2/R does not work is that neither 7 volts nor 2.25 volts is the voltage across the resistor. They are the voltages across the batteries.

    The voltage across the resistor is 9.25 volts.

    And for this value the formula works correctly.
     
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