Thevenin circuit Max power across Load resistor

AI Thread Summary
The discussion focuses on applying Thevenin's theorem to determine the maximum power across a load resistor (RL) in a circuit, which occurs when RL equals the Thevenin resistance (Rth). The power dissipated by the load resistor is expressed as P = I²RL, and participants suggest deriving this expression in terms of the circuit components. To find the maximum power, one must differentiate the power function with respect to RL and set the derivative to zero. The approach of solving for current (I) and substituting it into the power equation is confirmed as correct. Overall, the conversation emphasizes the importance of understanding circuit relationships and calculus in solving the problem.
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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