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Power and Power Dissipated by a resistor in layman's terms

  1. Dec 31, 2007 #1
    Can someone give me a reply Intro Physics style? :D

    P = IV is known as the "power of the circuit" right?

    But then, we have questions asking about the heat dissipated by a resistor. We can use P = IV, P=I^2 R , or P=V^2/R to answer such questions

    Since the voltage drops all add up to the original voltage.. won't adding IV + IV for each resistor yield the original Power... implying that ALL energy is dissipated as heat?

    I guess I don't understand the difference between the generic "Power" of the circuit and the power/head dissipated by resistors :(
  2. jcsd
  3. Dec 31, 2007 #2
    Yes, all energy goes into heat for a resistor.
  4. Dec 31, 2007 #3
    So ALL the energy is dissipated as heat?

    Isn't energy needed to run the circuit though?
  5. Dec 31, 2007 #4
    Think of a resistor's purpose in a way like a light bulb: a light bulb takes current and out comes some heat, but some light too, and less voltage out the other side because you used some of that energy to make heat and light. Now take away the light part. A resistor takes down your voltage, duh - but the energy has to go somewhere, ex. conservation of energy applies to voltages as well. So it comes off as heat, and this is very, very dependent on the resistance and voltage, because these things are a measure of how much energy goes in and comes out of a resistor.

    But also, not all of the current drops to zero; you can string multiple light bulbs and get varying amounts of light and heat to come out of them. So using a resistor effectively takes your voltage down a notch, by using some of that stored potential energy to heat up the resistor itself.
    Last edited: Dec 31, 2007
  6. Dec 31, 2007 #5


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    Staff Emeritus
    Science Advisor
    Gold Member

    No - at least nothing more than what is dissipated.

    If there was more energy supplied than energy lost, then with each looping of the circuit, the electrons would have a higher speed. You end up making energy out of nothing. Not allowed.
  7. Dec 31, 2007 #6
    A correction here: current isn't depleted after passing through a resistor or a light bulb. The same current enters the resistor as that which exits (by Kirchoff's laws). It is the voltage that is "diminished"; i.e. there is a potential drop from one side of the resistor to the other.
  8. Dec 31, 2007 #7
    Sorry for the confusion, I am a little rusty with the circuitry, and my edits = the slow. Further clarification:

    The set of equations mentioned, P = IV, P=I^2 R , or P=V^2/R are all a result of the first, namely using P=IV and substituting V=IR. These hold for voltages across either the entire circuit or individual resistors then. If you add up IV for each voltage drop per resistor, then you should get the entire power dissipated, if the entire circuit is composed of resistors: if all of the voltage drops across all of the resistors, then the energy comes out entirely as heat.
  9. Dec 31, 2007 #8
    Oh right... my bad

    That's the purpose of the Battery... to provide new voltage everytime

    So... as current travels through the circuit... energy has to be converted to another form.. in this case, heat .... at the end of the circuit, right before hitting the battery again, circuit energy is 0. However, it is replenished again with the voltage... am I getting it?
  10. Dec 31, 2007 #9
    Just remember that current and voltage are two separate but related parts of a circuit.

    The voltage is stored electric potential energy. It's the electrical version of potential gravitational energy; you put a ball high on a hill, it rolls down fast. You put it higher, it rolls faster.

    Current is a measure of how much electric charge you have moving. So to use the ball rolling, it is how many balls you have rolling. Current is the mechanism used to discharge the potential difference between the positive and negative sides of the battery.

    So if you put one or many resistors in any complicated configuration, you have the potential difference coming down after it passes a resistor - the balls roll down the hill, all the way to zero if you used up all the voltage. But your current is still conserved - you still have the same number of balls, even though some of them may have went in different directions, at the end of the day your current is conserved.
  11. Dec 31, 2007 #10


    Staff: Mentor

    I have only one thing to add to the previous comments. P=IV is the general relationship and works for all components including capacitors, inductors, and transistors. The other two relationships are just for resistors. Also, you can apply P=IV for a whole circuit or for any individual component.
  12. Dec 31, 2007 #11
    Sorry to bug you guys but:

    Electric power for transmission wires is "stepped up" to a very high voltage in order to:

    D) cut down heat loss in transmission wires

    there were other options.. just didn't include them

    If all the electric energy will be lost to heat in the resistors.. or wire... how can "heat loss" be reduced? Especially.. since the power of the circuit is fixed.

    This question is on the MCAT and since they only expect a basic conceptual understanding of the formulas, P = IV and V = IR... can somebody explain this conceptually using these formulas? Thanks
  13. Dec 31, 2007 #12
    If you envision the transmission line as a big resistor, you have a circuit that looks like an AC power supply connected to that big resistor. You could send the same amount of power through the line by having either low voltage/high current or high voltage/low current, or somewhere in between.

    Obviously, we would like to minimize the power lost to heat in our circuit (in our resistor). Since V=IR across our resistor circuit, and P=IV, our power lost to heat is P=I(IR)=(I^2)*R. By minimizing the current we have to pass through the line, we minimize the power lost to heat. This is why transmission lines step the voltage up to a high level.
  14. Dec 31, 2007 #13


    Staff: Mentor

    The point is that you want to deliver the power to the customer, not lose it in the transmission line. By using transformers you can basically deliver the power at any voltage that you like. Since the customer is in series with the transmission line the current is the same through both so to calculate the power lost you use P=I^2 R to determine the power lost in the transmission line. To minimize this for a fixed R you minimize I. To minimize I you maximize the delivered voltage.
  15. Jan 1, 2008 #14
    P = I * E

    E = V = voltage
    P = power
    I = current

    I like the PIE formula better because its easy to remember the word pie...

    If P stays the same then only I or E can change...so if you raise E then I must be reduced to keep P the same and vice versa...

    As someone states above the higher voltage for transmission lines is used to raise the efficency of the transmission lines by reducing the amount lost as heat because the current is lower to keep P the same...

    Using someone elses example above, the number of balls are reduced (lower current) and they are poured down a pipe on a taller hill (higher voltage) with fewer balls there is less congestion in the pipe and lower heat loss...

    Heat lose is reduced by raising the voltage...making the wire (resistor) more efficiant (less heat lose)...

    As a side note...most wiring today is copper, but what do you think transmission lines are made of?
    Aluminum...to keep the wires lighter...
    Last edited: Jan 1, 2008
  16. Jan 2, 2008 #15
    I guess I am getting confused between:

    Ohm's Law V = IR

    and Power

    I'm still a lil' confused....
    I understand if you increase V, I drops

    So if the resistance of the wire is "fixed".... I^2R = less than it was before

    But if the circuit has a fixed "power", I don't understand how I^R is changing.. if anyone can clear this up, I'd really appreciate it. According to a poster above, all the "power" of the circuit is transferred to heat...

    I thought Power Dissipated in the resistors should add up to the overall Circuit Power
    Last edited: Jan 2, 2008
  17. Jan 3, 2008 #16


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    Staff: Mentor

    Draw yourself a diagram. The power dissipated by the load is fixed, the power dissipated by the transmission lines is a function of voltage. So if you want to deliver a certain power with the least loss, you need a high voltage in the transmission lines.
  18. Jan 3, 2008 #17
    Depends what you're fixing. In a real circuit, the power of the implement creating the potential (battery, dynamo, black box, whatever) is generally fixed. Within this, you can set the voltage and current any way you like as long as combining them as I*V still equals the power rating of the 'box'. You could, of course, devise a black box power supply that always fixes the voltage - in which case the power dissipated by the circuit will vary instantaneously as you vary the current.
  19. Jan 3, 2008 #18


    Staff: Mentor

    There are two parts of the circuit: the transmission lines, and the load (customers). Power will be dissapated in both parts, but the power company only gets paid for the power dissapated in the load. The power dissapated in the transmission lines is wasted. The goal is to minimize this fraction of wasted power. Only the power to the load is considered fixed in this analysis, the power wasted in the transmission lines is considered variable.
  20. Jan 3, 2008 #19
    Thanks... I see how it makes sense common-sense wise... but mathematically, can someone confirm the following:

    Is it because in a normal circuit with a resistors and a battery, it's a closed circuit? everything that goes out comes back.

    However, with transmission lines, nothing ever comes back to the voltage source?

    In a simple circuit:

    P circuit = Sum of P lost at the resistors

    But with transmission lines:

    P circuit - P lost = P transmitted to people

    And you want to maximize P transmitted to people
    Last edited: Jan 3, 2008
  21. Jan 3, 2008 #20


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    Staff: Mentor

    Notice that your two equations are identical...

    With any circuit, the amperage is constant. It has to be. so whatever goes out comes back to the power company.
  22. Feb 6, 2008 #21
    let me explain this way:
    work done to move electorns from one potential to another is= E^2/R where E is the potintial diff

    For the same potential diff across transmission line, the work/ heat dissicipated will always be same. But with high voltage, you can maximize the power delivered to the load. that why high voltage transmission is better.

    Math: V1= source voltage V2 is the load voltage
    power lost in transmission=(V1-V2)^2/Rtx
    power delivered to load=V2^2/Rload

    Go figure what you need to maximize the efficiency.
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