What is Power dissipated: Definition and 72 Discussions

In electrical engineering, the maximum power transfer theorem states that, to obtain maximum external power from a source with a finite internal resistance, the resistance of the load must equal the resistance of the source as viewed from its output terminals. Moritz von Jacobi published the maximum power (transfer) theorem around 1840; it is also referred to as "Jacobi's law".The theorem results in maximum power transfer across the circuit, and not maximum efficiency. If the resistance of the load is made larger than the resistance of the source then efficiency is higher, since a higher percentage of the source power is transferred to the load, but the magnitude of the load power is lower since the total circuit resistance increases.If the load resistance is smaller than the source resistance, then most of the power ends up being dissipated in the source, and although the total power dissipated is higher, due to a lower total resistance, it turns out that the amount dissipated in the load is reduced.
The theorem states how to choose (so as to maximize power transfer) the load resistance, once the source resistance is given. It is a common misconception to apply the theorem in the opposite scenario. It does not say how to choose the source resistance for a given load resistance. In fact, the source resistance that maximizes power transfer from a voltage source is always zero, regardless of the value of the load resistance.
The theorem can be extended to alternating current circuits that include reactance, and states that maximum power transfer occurs when the load impedance is equal to the complex conjugate of the source impedance.
Recent expository articles illustrate how the fundamental mathematics of the maximum power theorem also applies to other physical situations, such as:

mechanical collisions between two objects,
the sharing of charge between two capacitors,
liquid flow between two cylinders
the transmission and reflection of light at the boundary between two media

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  1. guyvsdcsniper

    Graphing the Power dissipated in a resistor

    I am solving #5 in the attached image. So I am graphing the power dissipated by a series circuit which : (a) Contains a constant voltage source and a variable resistor, R (b) Contains a constant current source and a variable resistor. It makes sense to me to just use the power equation that...
  2. G

    Power dissipated by a resistor on a coaxial cable

    I need help with part c. My solution: Is there an other way to do this other than dimensional analysis? P.S "dr an infinitesimal radius", it ofcourse should be dz.
  3. patric44

    Power dissipated in this circuit with 2 batteries and 3 resistors

    Hi guys I am struggling to find the power dissipated in the total circuit , my answer didn't match the solution in the book the circuit is simple i used Kirchhoffs rules to find the following : loop 1 : $$10-10I_{1}-40I_{3} = 0$$ loop 2: $$20-20I_{2}-40I_{3} = 0$$ and $$ I_{1}+I_{2}=I_{3}$$...
  4. D

    Joule heating effect - qualitative explanation

    Hi, I understand mathematically why using low resistance results in a greater heating effect. Could someone give an intuitive and microscopic picture of why the current contributes more to a greater power dissipation by the resistor rather than the resistance contribution to the power...
  5. A

    Active power dissipated by a resistor from DC to RF

    Hello all PF members! I was wondering about the power dissipated by resistor at high frequency which is: ##P=Re\left \{ U\cdot I^{*} \right \}=Re\left \{ \frac{\left |V^{+} \right |^{^{2}}}{2\left |Z_{c} \right |}\cdot (1-\left |\Gamma \right |^{2} )\right \}##, (1) where: ##Z_{c}## -...
  6. marino

    Power generated by a coil rotating in magnetic field

    The problem: a coil of radius r, length l and N turns, rotating with constant angular velocity ω around an axis perpendicular to its simmetric axis and passing for the center of the coil. The coils is submersed in a static magnetic field, intensity B0, perpendicular to the axis of rotation of...
  7. A

    Power dissipated by a Resistor

    Homework Statement What power is dissipated by the R2=3.0Ω resistor in the figure if R1=6.0Ω? Battery 1: 12 V Battery 2: 15 V Resistor 1: 3.0 Ω Resistor 2: 6.0 Ω Homework Equations P = V2/R Rtotal = R1 + R2 The Attempt at a Solution I started on the left side and used the formula, P = V2/R...
  8. J

    Power dissipated in a resistor

    Homework Statement Homework EquationsThe Attempt at a Solution Power dissipated in the 2 Ohms resistor will be maximum when current is maximum .This will occur when total resistance is minimum . If I think logically then I do get the right answer . But on trying to arrive at the result...
  9. J

    Power dissipated across a transistor regulator

    Homework Statement [/B]Homework Equations For the 1st part Ohms law and resistance across zener is 10V[/B] I can't get 2nd The Attempt at a Solution For 1st part I took Vi/p = 18V[/B] Putting KVL for left loop of source-->collector-->base-->zener-->ground 18 = Vcb + 10 So Vcb = 8V And Vbe =...
  10. R

    Filament lamp model (derivation)

    Homework Statement State and use simple assumptions to show that ' Power is proportional to V^5' is the expected relationship for a pure tungsten filament bulb. Homework Equations V=IR I=dq/dt Q=mcT The Attempt at a Solution I tried to use a simple model where the rate of heat loss is...
  11. M

    Power Dissipated By Resistor is LRC Circuit

    [Note by mentor: this post does not use the homework template because it was originally posted in a non-homework forum.] --------------------------------------------- Problem: What is the average power dissipated by a 25-Ω resistor in an LRC series ac circuit for which the power factor is...
  12. J

    Finding I1, I2, and power dissipated

    Homework Statement See attatched image Homework Equations I am assuming to use the current divider rule... But when I use it, I do not get the correct answer 1/Rt = 1/R1 + 1/R2 + 1/R3 .. When I used this I got Rt= 2.18 ohms I also tried Is= E/Rt... 24/2.18 =11 AI am not sure what to try...
  13. kamhogo

    What happens to the total power dissipated in the circuit ?

    Homework Statement What happens to the total power dissipated in the circuit once the switch is closed? Homework Equations Pr=Pbat=dEth/dt=(dq/dt)*Vr=I*Vr[/B]The Attempt at a Solution V total and I toral remain the same so the power dissipated by the circuit stays the same...?
  14. Silverado

    Power Dissipated in a Sliding Resistor

    Homework Statement The circuit [http://tinypic.com/r/2cwl7bt/9] shows a battery connected across a uniform resistor R0. A sliding contact can move across the resistor from x = 0 at the left to x = 10 cm at the right. Find an expression for the power dissipated in the resistor R as a function...
  15. kostoglotov

    Energy dissipated by a loop of muscle in an MRI machine

    edit: turned out to be a calculator typo...mods feel free to delete this thread if you wish, I won't complain. Homework Statement [/B] Having issues with part a) imgur link: http://i.imgur.com/4hzLyhb.jpg Homework Equations Resistivity of muscle (from table in text): \rho \approx 13...
  16. V

    Power loss when fan is connected; finding current

    Homework Statement An electric fan which is plugged into a 115 V(rms), 60 Hz socket in your house can be considered as made up of a 1500 Ω resistor in series with a 1.4 H inductance. How much power is dissipated by this electric fan on the average? (in W) Homework Equations P = IV = I^2 R I =...
  17. kostoglotov

    Power dissipated by resistor -- Right answer, but need insight

    imgur: http://i.imgur.com/9VILpYL.jpg Now, I can easily solve this by applying the formula P_R = \frac{(\Delta V_R)^2}{R} and get all the correct answers. However, the answers feel strange to me intuitively. In the formula above, lowering the resistance increases the power that is dissipated...
  18. J

    Power Dissipation in a Resistor: How Does Resistance Affect Energy Loss?

    Homework Statement Homework Equations P=V2/R P=I2R V=IR The Attempt at a Solution As the resistance of R increases, the potential difference across R increases, so the power dissipated in R increases too. But I can't seem to see how the power decreases afterwards. Is it because, as time passes...
  19. toforfiltum

    Mean power dissipated in resistor in ac circuit

    Homework Statement Homework EquationsThe Attempt at a Solution I am surprised that this question came up, I haven't learned ac circuits yet. I don't know how to solve this. I just added both values and current and divide it by two, which gives me 1.5A, since I thought it's the average but I'm...
  20. P

    Find power dissipated in circuit with a ground

    Homework Statement 1. Find the power dissipated by 12 ohm resistor 2. What is the potential at points a,b,c,d? Homework Equations P=I^2R I=V/R The Attempt at a Solution For a) 3v-IR-6v-IR=0 9v=I(18) I=0.5 P=0.5^2 * 12 = 3 watts But not sure if the ground changes anything b) unsure if ground...
  21. skepticwulf

    Understanding Power Dissipation in Electric Wires

    In a general homework question I often encounter terms like "a wire of resistance R is stretched, what factor the power dissipated changes?" What exactly is this power dissipated ? Is it the one "wasted away" by heating up the wire due to the wire's resistance? or is it the power "used up" or...
  22. estike

    Power Dissipated by 60W Bulb in 20V Source[/B]

    Homework Statement What is the power dissipated by a 60 Watt (rated at 120 V) light bulb if it is connected to a 20 V power source (assume the resistance of the bulb is constant)? Homework EquationsThe Attempt at a Solution If it [/B]
  23. CAH

    Power dissipated in variable resistor?

    See photo! Why does the power dissipated increase and then decrease (see graph)? Is it something to do with emf? Also can internal resistance change as the variable resistor increases/decreases or is it always constant? - this isn't one of the questions they ask I'm just wondering
  24. B

    Average power dissipated in resistor

    Homework Statement Find the average power dissipated in the 30 Ω resistor in the circuit seen in the figure if ig=7cos20,000tA. Homework Equations KVL/KCL equations P=VI* (possibly) or I^2(R) The Attempt at a Solution I tried to do a mesh, but got I∆(60-j130) = 0, which isn't right . . . I'm...
  25. Valkarie

    Figuring out the split for power dissipated?

    Hello everyone! This is my first post, I've done a bunch of searching on this forum which has yielded me quite positive results, so thank you for all of your posts which are a bloody gold mine of information. Although I've gotten quite a lot of information that has been useful, I'm still...
  26. P

    Power dissipated by a resistor in a circuit

    Homework Statement Homework Equations P = V^2 / R 1/Rt = sum(1/Ri) (parallel) The Attempt at a Solution [/B] Since all the answer choices express the solution in terms of V^2 / R, I tried to find the voltage drop across resistor #2 to find the power. I collapsed the two parallel...
  27. U

    Power dissipated by a resistor in combined citcuit

    Find the power dissipated by R2 given that V a-b=120 volts, R1=1, R2=3.33, R3=2, and R4=3 I've worked this problem, just want to confirm I worked it correctly. A---------R1-----------*------------------- | |...
  28. A

    How Does Adding a Resistor Affect Power Dissipation in a Parallel Circuit?

    Homework Statement You have a circuit with a single resistor of resistance R connected to a battery that has zero internal resistance and has a power output of 12W. A resistor of resistance of 6R is now connected in parallel to the original resistor. How much power is now dissipated in the...
  29. S

    Triac - Power dissipated in light bulb

    Homework Statement A triac is used in a dimmer switch to control a 100W light bulb. If the firing angle is set for α=∏/3 estimate the power dissipated in the bulb Rated at 100W and the voltage source 230V @ 50Hz. Homework Equations Vpeak = Vrms/0.707 The Attempt at a Solution...
  30. P

    Power dissipated in an RL circuit

    Homework Statement a) A circuit contains two elements, but it is not known if they are L, R or C. The current in this circuit when connected to a 2.16×102 V, 60.0 Hz source is 6.10 A and lags the voltage by 3.60×10^1 degrees. What are the two elements? c) What is the power dissipated in...
  31. Z

    Power dissipated in circuit: What is the total power dissipated in this circuit?

    Homework Statement Use the node-voltage method to find the total power dissipated in the circuit in the figure if i1 = 2A , i2 = 3A and v1=16V Homework Equations P = iv v = iR P = v^2/R G = 1/R \sumG connected to node 1 * v_1 - \sumG between node 1 and 2 * v_2 = Current source into node...
  32. P

    Power dissipated and current of a battery in a particular circuit

    Homework Statement Four resistors are connected in a circuit with a battery of unknown emf, as shown below. The battery is ideal, so it has no internal resistance. The current in the 30Ω resistor is 100. milliamps. C) Calculate power dissipated by the 20Ω resistor in watts. D)Calculate the...
  33. A

    Engineering Power dissipated in circuit combination

    Homework Statement three resistors R1=R2 and R2=2R3, are connected to a battery, as show in the figure, if the power dissipated for each one is p1,p2 and p3 respectirvely;p3 must be equal to: Homework Equations P=VI P=V^2/R P=I^2*R The Attempt at a Solution I have tried to...
  34. A

    What happens to the power dissipated in a resistor when the voltage ac

    What happens to the power dissipated in a resistor when the voltage across it is changed?
  35. A

    Change in watts and power dissipated

    One of my homework questions is giving me trouble: "In, the US, the rms voltage from power outlets (known as line voltage) is 120 V. In the United Kingdom, line voltage is 230 V. If you take a lamp with a standard 100 W incandescent light bulb from the US, how much power will it dissipate if...
  36. F

    Voltage effects on power dissipated

    Trying to find the relationship between voltage and power across a resistive something. Using a lightbulb if the bulb was rated at 100W when 140 Volts is used, what would happen to the power if the voltage was doubled? (assuming the light bulb doesn't explode)
  37. E

    Power Dissipated on light bulb

    1. A 25 ohm resistor is connected in series with a 100 W light bulb. The standard 120V/60Hz AC outlet voltage is applied to the series combination. Determine the real power dissipated on the light bulb. Assume the internal resistance of the light bulb is independent of the power dissipation...
  38. A

    Power dissipated by a resistor in parallel

    Homework Statement We are given a circuit as follows: V= 10 V and two resistors are in parallel. R1 is 12 ohms and R2 is 5 ohms. What is the power dissipated in the 12 ohm resistor? Homework Equations V=IR P=(I^2)R The Attempt at a Solution I know that the total resistance of...
  39. A

    What is total equivalent resistance and power dissipated?

    Another one.. I'm sorry but I will likely spend tomorrow and today here with you guys asking for help and mooching solutions. Same deal, badly explained unit. We spent 15 minutes on this. Attached questions as jpg... Homework Statement How do I find total equivalent resistance? What does...
  40. C

    Using Kirchhoff's Laws to Find Currents, Source Current and Power Dissipated

    Homework Statement In the circuit shown in Figure Q8 below, if Vs = 10V, use Kirchoff’s Laws to determine the currents i1, i2, i3 and the source current is. Calculate the power dissipated by the resistors in this circuit. Confirm that the power dissipated by the resistors is the same as the...
  41. B

    Power dissipated from resistance

    Homework Statement This was a diagram, so I will describe it as accurately as possible. [Edit]: 12 Volts go through one 2 Ohm resistor which then proceeds through a set of resistors in parallel. One is 20 Ohms, the other two are 10 Ohms. How much power is being dissipated by one of the 10...
  42. L

    Power Dissipated for 2 different circuits

    Part A: For what ratio of R1 and R2 would power dissipated by the resistor of resistance R2 be the same for circuit A and circuit B? current for R2 of circuit A is (2EMF)/(2R1+R2) current for R2 of circuit B is (EMF)/[(R1^2/2R1) + R2) Part B: Under which of the following conditions would power...
  43. A

    Power supply and power dissipated in a circuit

    Can Power supply be smaller than power dissipated? Because I saw this in one question There are 3 cells, the power supply of the two 4V cells cancel each other. (one is -4W and another one is 4W) So the total power supply should be 16W But in part c, the power dissipated is 4+8+2+6=20W...
  44. P

    To double the power dissipated by a resistor you can

    Homework Statement 1) double the potential difference, ΔV 2) double the current, I 3) reduce the resistance, R, by 1/2 Homework Equations The Attempt at a Solution These problems are usually straightforward but I'm a little confused this time because I keep seeing all of the...
  45. S

    Power Dissipated by a Lightbulb

    1. The electric power P is dissipated by a light bulb of resistance R is P=v^2/R, where V represents the line voltage. During a brownout, the line voltage is 10.0% less than its normal value. How much power is drawn by a light bulb during the brownout if it normally draws 100.0 W (watts)? Assume...
  46. S

    Power Dissipated In a Linear Damper

    Hello, I have a question about power dissipated in a linear damper. I know that power is equal to force times velocity, and that force is equal to the damper coefficient times velocity. What I have to work with is the coefficient and the velocity of the damper, so the instantaneous power...
  47. S

    Power dissipated by a resistor

    hi just needed to know if the power dissipated by a resistor is equal to the total voltage. I am having a hard time understanding a problem i was given, and i know the formulas to find power dissipated, but i can't use P = I squared * R or P = V squared / R for this question... " A 10 ohm...
  48. P

    Expression for the time average power dissipated in a resistance R

    Homework Statement A square loop with side-length a is positioned at the centre of a long thin solenoid, which has radius r (with r > a), length l and N turns. The plane of the loop is perpendicular to the 5axis of the solenoid. A current I = I0 sin ωt flows through the loop. Derive an...
  49. F

    Find the value of Vx and power dissipated

    Homework Statement I'm looking to find the value of Vx and power dissipated or provided by the dependent source. Homework Equations I used KVL to get around the loop, but I'm not sure if that's correct. The Attempt at a Solution The main loop I get 10+3Va+10kI = 0. No clue what to do...
  50. C

    Show that power supplied = power dissipated

    Show that "power supplied" = "power dissipated" Homework Statement For the circuit of Fig. 3-42, show that the power supplied by the sources is equal to the power dissipated in the resistors. Ans. P_T=940.3\text{ }W [PLAIN]http://img269.imageshack.us/img269/2010/dsc01005kn.jpg Homework...