Thevenin circuit Max power across Load resistor

[EricSomin]

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 R_L = R_th. 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.

 

[gneill]

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 R_L = R_th. 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 R_L: P(R_L) = ...

Find the maximum w.r.t. R_L.

 

[EricSomin]

I think I've figured it out. I can solve for I, input that into

P=I²R_L

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

does this sound incorrect to anyone?

 

[gneill]

I think I've figured it out. I can solve for I, input that into

P=I²R_L

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

does this sound incorrect to anyone?

Nope. Sounds like a good plan.