Thevenin circuit Max power across Load resistor

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Homework Help Overview

The discussion revolves around applying Thevenin's theorem to determine the maximum power transfer across a load resistor in an equivalent circuit. The original poster seeks guidance on how to prove that maximum power occurs when the load resistor equals the Thevenin resistance.

Discussion Character

  • Exploratory, Assumption checking

Approaches and Questions Raised

  • The original poster expresses uncertainty about how to begin the problem and seeks direction. They mention understanding Thevenin circuits and the placement of load resistors but require assistance in formulating a strategy. Another participant suggests drawing the circuit and deriving an expression for power in terms of the load resistor.

Discussion Status

Some participants are exploring the relationship between current and power in the load resistor. One participant proposes taking the derivative of the power expression to find the maximum, and another agrees with this approach, indicating a productive direction in the discussion.

Contextual Notes

The original poster has indicated a lack of initial direction and is looking for foundational steps to approach the problem. There is a focus on deriving expressions and understanding the conditions for maximum power transfer.

EricSomin
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Homework Statement



One Thevenin theorem result is that the maximum power across the load resistor in the equivalent circuit (and therefore the real circuit) occurs when RL = Rth. Start with the result that the power dissipated by the load resistor is I2RL and prove this result.

Homework Equations





The Attempt at a Solution



I have really no idea where to begin with this question. I do understand what a Thevenin circuit is, and where i would place a load resistor. I am just looking for some direction as to where to start, or for someone to point me towards what i should be thinking about and working with to get towards an answer.

any help or thoughts would be greatly appreciated.
 
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EricSomin said:

Homework Statement



One Thevenin theorem result is that the maximum power across the load resistor in the equivalent circuit (and therefore the real circuit) occurs when RL = Rth. Start with the result that the power dissipated by the load resistor is I2RL and prove this result.

Homework Equations





The Attempt at a Solution



I have really no idea where to begin with this question. I do understand what a Thevenin circuit is, and where i would place a load resistor. I am just looking for some direction as to where to start, or for someone to point me towards what i should be thinking about and working with to get towards an answer.

any help or thoughts would be greatly appreciated.

Draw the circuit. Obtain an expression for the power in the load in terms of the given components, yielding the power as a function of RL: P(RL) = ...

Find the maximum w.r.t. RL.
 
I think I've figured it out. I can solve for I, input that into

P=I2RL

Since I am trying to max. power dissipated by RL i can take the first derivative and set it equal to zero.

does this sound incorrect to anyone?
 
EricSomin said:
I think I've figured it out. I can solve for I, input that into

P=I2RL

Since I am trying to max. power dissipated by RL i can take the first derivative and set it equal to zero.

does this sound incorrect to anyone?

Nope. Sounds like a good plan.
 

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