Why Doesn’t Load Power Keep Increasing with Load Resistance?

In summary: However, once RL reaches a certain point (depending on the circuit and the source), power begins to drop. This is because the current through the load is no longer large enough to keep up with the power dissipated by the load.
  • #1
JJBladester
Gold Member
286
2

Homework Statement



"If the load voltage at the output of a circuit keeps going up as the load resistance is increased, why doesn’t the load power keep going up as well?"

Homework Equations



The maximum power transfer theorem states:
A load will receive maximum power from a network when its resistance is exactly equal to the Thevenin resistance of the network applied to the load. That is,

RL=Rth

max_power.JPG


RL = Load resistance

PL = Power dissipated by load

Rth = Thevenin resistance

[tex]I_L=\frac{E_{th}}{R_{th}+R_L}=\frac{E_{th}}{R_{th}+R_{th}}=\frac{E_{th}}{2R_{th}}[/tex]

[tex]P_{L_{max}}=I_{L}^{2}R_L=\left (\frac{E_{th}}{2R_{th}} \right )^{2}\left (R_{th} \right )=\frac{E_{th}^{2}R_{th}}{4R_{th}^{2}}=\frac{E_{th}^{2}}{4R_{th}}[/tex]

The Attempt at a Solution



Here's how I answered this question.

The power *will* keep going up until RL = Rth. The graph of PL versus RL reaches a maximum (d/dRL = 0) at that point. Thereafter, PL will gradually decline as R approaches infinity.

R approaching infinity is analogous to an open circuit in which no current can flow. With no current flow, there can be no power.

That's how I answered the question, but I'm not fully satisfied with my answer. Maybe I'm actually not satisfied with the wording of the original question... A Thevenin voltage source wouldn't change; it would be fixed, right? Thus, this question is sort of mis-stated in my opinion.

Doesn't the maximum power transfer theorem assumes a fixed source voltage?
 
Physics news on Phys.org
  • #2
I think your answer is fine. When the load resistance increases past the source resistance, less current flows throught the load, reducing the power dissipated.

BTW, have you learned yet that for circuits with reactive components (like inductors and capacitors), the maximum power transfer occurs when the load impedance is the complex conjugate of the source impedance? When the circuit only has resistors, there is no imaginary component to the impedances, so maximum power is transferred when the resistances are equal.
 
  • #3
berkeman said:
I think your answer is fine.

Thank you. I'm still curious whether the maximum power transfer theorem is applicable if the source voltage is allowed to increase. My understanding of a Thevenin circuit was that Eth was *fixed*.

berkeman said:
BTW, have you learned yet that for circuits with reactive components (like inductors and capacitors), the maximum power transfer occurs when the load impedance is the complex conjugate of the source impedance?

Berkeman, I haven't learned this yet. We just got into capacitors. I'm excited to learn about the M.P.T.T. for cases other than simply resistors!
 
  • #4
JJBladester said:
Thank you. I'm still curious whether the maximum power transfer theorem is applicable if the source voltage is allowed to increase. My understanding of a Thevenin circuit was that Eth was *fixed*.

The source is usually a fixed value for these calculations. I'm not sure what it means for the source voltage to be "allowed" to increase. Sources are usually fixed, unless they have some strange behavior. They can be current limited, for example, as many real power supplies are. But that will result in a decrease in output voltage if the current limit is reached...
 
  • #5
The initial statement of the problem said that the load voltage rises as the load resistance rises, which is perfectly true for even a fixed value of Eth; in the limit as RL approaches infinite resistance the load voltage approaches Eth.
 

FAQ: Why Doesn’t Load Power Keep Increasing with Load Resistance?

What is the Maximum Power Transfer Theorem?

The Maximum Power Transfer Theorem is a principle in electrical engineering that states that maximum power will be transferred from a source to a load when the resistance of the load is equal to the resistance of the source.

Why is the Maximum Power Transfer Theorem important?

The Maximum Power Transfer Theorem is important because it allows engineers to determine the optimal resistance for a load in order to achieve maximum power transfer. This is useful in designing efficient electrical circuits.

What are the assumptions of the Maximum Power Transfer Theorem?

The Maximum Power Transfer Theorem assumes that the source and load are both linear and that the source is an ideal voltage source with no internal resistance. It also assumes that the load is a resistive load.

Can the Maximum Power Transfer Theorem be applied to AC circuits?

Yes, the Maximum Power Transfer Theorem can be applied to AC circuits as long as the source and load are both linear and the load is purely resistive. In this case, the resistance referred to is the effective resistance, which takes into account the reactive components of the circuit.

What is the formula for calculating the maximum power transfer using the Maximum Power Transfer Theorem?

The formula for calculating the maximum power transfer using the Maximum Power Transfer Theorem is Pmax = (Vsource2 / 4Rsource), where Pmax is the maximum power, Vsource is the source voltage, and Rsource is the source resistance.

Back
Top