Thevenin circuit Max power across Load resistor

Click For Summary
SUMMARY

The discussion centers on applying Thevenin's theorem to determine the maximum power transfer across a load resistor (RL) in an equivalent circuit. The key conclusion is that maximum power occurs when the load resistor value equals the Thevenin resistance (Rth). Participants suggest starting by deriving the power formula P = I²RL and then finding its maximum by taking the derivative with respect to RL and setting it to zero. This method is confirmed as a valid approach by other forum members.

PREREQUISITES
  • Thevenin's Theorem
  • Basic circuit analysis
  • Calculus (specifically differentiation)
  • Understanding of load resistors in electrical circuits
NEXT STEPS
  • Study Thevenin's theorem applications in circuit analysis
  • Learn how to derive power equations in electrical circuits
  • Practice taking derivatives to find maxima in power functions
  • Explore real-world applications of maximum power transfer in electrical engineering
USEFUL FOR

Electrical engineering students, circuit designers, and anyone interested in optimizing power transfer in electrical circuits.

EricSomin
Messages
9
Reaction score
0

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.
 
Physics news on Phys.org
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.
 

Thread 'Magnitude of buoyant force in fluids of different densities'

The book claims the answer is that all the magnitudes are the same because "the gravitational force on the penguin is the same". I'm having trouble understanding this. I thought the buoyant force was equal to the weight of the fluid displaced. Weight depends on mass which depends on density. Therefore, due to the differing densities the buoyant force will be different in each case? Is this incorrect?
View full post »

Similar threads

Maximum Power dissipated at load resistor
  • · Replies 3 ·
Replies
3
Views
1K
Finding the value of this load resistor
  • · Replies 2 ·
Replies
2
Views
1K
Thevenin Theorum
  • · Replies 1 ·
Replies
1
Views
2K
Electrical Network Problem: Power Transfer
  • · Replies 9 ·
Replies
9
Views
2K
What is the Thevenin and Norton equivalent for the given circuit in Fig. 4.125?
  • · Replies 10 ·
Replies
10
Views
3K
How Do You Calculate Thevenin Equivalent Circuit Without a Load Resistor?
  • · Replies 3 ·
Replies
3
Views
2K
Find resistance of resistor in RC circuit
  • · Replies 4 ·
Replies
4
Views
2K
Power dissipated in this circuit with 2 batteries and 3 resistors
  • · Replies 22 ·
Replies
22
Views
4K
Thevenin's circuit analysis. Multiple voltage sources
  • · Replies 6 ·
Replies
6
Views
2K
Thevenin equivalent for an AC circuit
  • · Replies 10 ·
Replies
10
Views
3K