Maximizing dissipation rate


by Granite
Tags: dissipation, maximizing, rate
Granite
Granite is offline
#1
Nov24-08, 12:59 PM
P: 4
QUESTION:
R1 = 2 ohm
R2 = 5 ohm
What value of R3 maximizes the dissipation rate in resistance 3? (battery is ideal -> no internal resistance)

DIAGRAM:
_______________
|.........|...........|
R1.......R2.........R3
|.........|...........|
_ +......|...........|
- -.......|...........|
|.........|...........|
_______________


Someone posed this question on the forums years ago, but the answer wasn't entirely helpful. I couldn't reconcile some missing pieces of information.

I've established that the equivalent resistance in the whole circuit (expressed in terms of R3) is:

(7R3 + 10)/(R3 + 5)

I know that the power is maximized when the derivative of the power function is equal to zero, but the distinct absence of current is holding me back. I've also tried to use Kirchoff's laws to establish some equations to solve for current, but it introduces three new unknown values and several of the equations render themselves useless upon application.

Can someone help me with this?
Phys.Org News Partner Science news on Phys.org
SensaBubble: It's a bubble, but not as we know it (w/ video)
The hemihelix: Scientists discover a new shape using rubber bands (w/ video)
Microbes provide insights into evolution of human language
Redbelly98
Redbelly98 is offline
#2
Nov24-08, 09:22 PM
Mentor
Redbelly98's Avatar
P: 11,989
Welcome to PF!

How about getting the total current using the equivalent resistance?
Granite
Granite is offline
#3
Nov24-08, 09:27 PM
P: 4
Ah.

Yeah. I don't know where my mind was at...but I determined the solution.

Thanks.

Consider this question SOLVED.


Register to reply

Related Discussions
Maximizing Calculus & Beyond Homework 0
Maximizing revenue Calculus 1
Average rate of energy transfer & rate of energy dissipation. Introductory Physics Homework 4
dissipation Introductory Physics Homework 0
maximizing dissipation rate in a simple circuit Introductory Physics Homework 5