Maximizing Dissipation Rate in a Three-Resistance Circuit

  • Thread starter Thread starter Granite
  • Start date Start date
  • Tags Tags
    Dissipation Rate
AI Thread Summary
To maximize the dissipation rate in resistance R3 of a three-resistance circuit with R1 at 2 ohms and R2 at 5 ohms, the equivalent resistance can be expressed as (7R3 + 10)/(R3 + 5). The power dissipation is maximized when the derivative of the power function equals zero, which requires determining the total current using the equivalent resistance. The original poster struggled with the calculations but ultimately found the solution after reconsidering their approach. The question is now resolved.
Granite
Messages
4
Reaction score
0
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?
 
Physics news on Phys.org
Welcome to PF!

How about getting the total current using the equivalent resistance?
 
Ah.

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

Thanks.

Consider this question SOLVED.
 

Thread 'Struggling to understand the concept of this question (ice cube in water optics question)'

TL;DR Summary: I came across this question from a Sri Lankan A-level textbook. Question - An ice cube with a length of 10 cm is immersed in water at 0 °C. An observer observes the ice cube from the water, and it seems to be 7.75 cm long. If the refractive index of water is 4/3, find the height of the ice cube immersed in the water. I could not understand how the apparent height of the ice cube in the water depends on the height of the ice cube immersed in the water. Does anyone have an...
View full post »
Thread 'Variable mass system : water sprayed into a moving container'

Thread 'Variable mass system : water sprayed into a moving container'

Starting with the mass considerations #m(t)# is mass of water #M_{c}# mass of container and #M(t)# mass of total system $$M(t) = M_{C} + m(t)$$ $$\Rightarrow \frac{dM(t)}{dt} = \frac{dm(t)}{dt}$$ $$P_i = Mv + u \, dm$$ $$P_f = (M + dm)(v + dv)$$ $$\Delta P = M \, dv + (v - u) \, dm$$ $$F = \frac{dP}{dt} = M \frac{dv}{dt} + (v - u) \frac{dm}{dt}$$ $$F = u \frac{dm}{dt} = \rho A u^2$$ from conservation of momentum , the cannon recoils with the same force which it applies. $$\quad \frac{dm}{dt}...
View full post »

Similar threads

Power dissipated in this circuit with 2 batteries and 3 resistors
Replies
22
Views
4K
Total equivalent resistance of a combined circuit
Replies
7
Views
2K
The equivalent resistance for the resistors in this circuit?
Replies
5
Views
2K
Electrical Circuits - Parallel vs. Series
Replies
14
Views
1K
How to solve this chain with Kirchhoff's laws?
Replies
18
Views
3K
Total Resistance of Parallel Circuit Calculation
Replies
3
Views
1K
Platinum resistance thermometer and Kirchoff's Laws
Replies
1
Views
3K
Parallel circuit with internal resistance
Replies
6
Views
2K
Voltage, Current, and Resistance Calculations
Replies
13
Views
2K
Calculating total resistance of a combination circuit
Replies
19
Views
7K

Hot Threads

Recent Insights

Back
Top