What is the maximum power of the variable resistor R?

Click For Summary
SUMMARY

The maximum power of the variable resistor R in the given circuit can be determined using the principles of electrical engineering. For part (a), the calculated value of R is 2.5 ohms, ensuring that each of the two 10Ω resistors dissipates 10W. For part (b), to find the value of R that allows for maximum power dissipation, one must apply the maximum power transfer theorem, which states that maximum power is transferred when the load resistance equals the source resistance. This requires further calculations involving the current through R and the parallel resistors.

PREREQUISITES
  • Understanding of Ohm's Law
  • Familiarity with the maximum power transfer theorem
  • Basic knowledge of series and parallel resistor circuits
  • Ability to perform calculus for optimization problems
NEXT STEPS
  • Study the maximum power transfer theorem in detail
  • Learn how to calculate power dissipation in resistors
  • Explore optimization techniques in calculus
  • Review circuit analysis involving series and parallel configurations
USEFUL FOR

Electrical engineering students, hobbyists working with circuits, and anyone interested in optimizing resistor configurations for maximum power dissipation.

headshrinker
Messages
18
Reaction score
0

Homework Statement



(a) For the circuit below, the value of R is adjusted so that each of the two 10Ω resistors dissipates 10W. Calculate the value of the variable resistor R.

(b) What is the value of R if it is adjusted to dissipate the maximum power possible? For this value of R, determine the current through the resistor R and through each of the parallel 10Ω resistors.

Homework Equations





The Attempt at a Solution



I've done part (a) and found the value of R to be 2.5ohms. i have no idea how to do part (b). can anyone help?!

Thank you!
 

Attachments

  • resistor.jpg
    resistor.jpg
    4.9 KB · Views: 414
Physics news on Phys.org
If you know what R is, what is the power dissipated in this resistor? (as a function of R)
do you know any method for finding the maximum value of a function?
 
i have no idea! I am new to this stuff! do u know?

thanks!
 
anyone?
 

Similar threads

Graphing the Power dissipated in a resistor
  • · Replies 1 ·
Replies
1
Views
2K
Spherical Capacitor Discharging Through Radial Resistor
  • · Replies 2 ·
Replies
2
Views
2K
Maximum Power dissipated at load resistor
  • · Replies 3 ·
Replies
3
Views
1K
How Do You Determine the Load Resistor Value for Maximum Power Dissipation?
  • · Replies 25 ·
Replies
25
Views
4K
GR- effective potential, maximum attainable radius
  • · Replies 1 ·
Replies
1
Views
2K
How Does Radioactive Decay Affect Current in a Spherical Capacitor Circuit?
  • · Replies 5 ·
Replies
5
Views
2K
Types of circuits that have a nonlinear response to R
  • · Replies 29 ·
Replies
29
Views
2K
Current through a lightbulb after flowing through transistor
  • · Replies 10 ·
Replies
10
Views
3K
Undergrad Is the Poynting Vector Field the Only Factor in Energy Flow in Circuits?
  • · Replies 16 ·
Replies
16
Views
3K
Engineering Intro to Power Systems: AC RLC circuit voltage calculations
  • · Replies 17 ·
Replies
17
Views
3K