Rank Resistors by Energy Dissipation: 5Ω > 10Ω > 20Ω > 90Ω

[mattbeatlefreak]

Homework Statement

Rank the resistors according to to the rate at which energy is dissipated in them.

Homework Equations

P = I²R
P = V²/R
I_in=I_out at a node

The Attempt at a Solution

First I looked considered the 20 Ω (top) and the 10 Ω(bottom). The current in them would be the same, so then applying the equations you get that the energy dissipated in the 20 Ω(top) > 10 Ω(bot).
Next I looked at the 10, 5, and 20 Ω resistors in parallel. Resistors in parallel have the same voltage. Therefore, I concluded that the energy dissipated in the 5 Ω > 10 Ω > 20 Ω.
Again I was thinking that the voltage would be same in the two 90 Ω resistors, so I have their energy dissipated equal, 90Ω(left) = 90Ω(right).

I think I did that part right. However, I do not know how to go about comparing these three sets. I feel that it would be 5Ω > 10Ω > 20Ω > 90Ω = 90Ω > 20Ω(top) > 10Ω(bottom) since parallel circuits take more energy than a series configuration. Does this look correct? Thanks in advance for any help!

 

[Passionate Eng]

find the equivalent of each parallel combination to reduce the circuit to a single mesh
the resultant of (10,5,20) will be less than 5 so it will absorb the least amount of power
(90,90)--> 45, the most amount.
______________________________
"parallel circuits take more energy than series" you said, this is right when you are talking about the same resistors
if connected (10,5,20) in series with a 5V voltage source they well absorb less power than if they are connected in parallel

 

[mattbeatlefreak]

find the equivalent of each parallel combination to reduce the circuit to a single mesh
the resultant of (10,5,20) will be less than 5 so it will absorb the least amount of power
(90,90)--> 45, the most amount.

The equivalent resistance from the 10,5,20 is approximately 2.86 ohms, and for 90,90 is, as you said, 45 ohms. So you're saying that the order would then be [90=90]>20(top)>10(bottom)>[5>10>20]?

 

[Passionate Eng]

exactly

 

[SammyS]

The equivalent resistance from the 10,5,20 is approximately 2.86 ohms, and for 90,90 is, as you said, 45 ohms. So you're saying that the order would then be [90=90]>20(top)>10(bottom)>[5>10>20]?

The equivalent resistance from the 10,5,20 is approximately 2.86 ohms, and for 90,90 is, as you said, 45 ohms. So you're saying that the order would then be [90=90]>20(top)>10(bottom)>[5>10>20]?

That is the correct order. The analysis you have looks a bit shy of actually showing that order, unless I missed something.

For instance, if there was a 30 Ω resistor replacing the 20 Ω resistor the order would be different.

The pair of 90 Ω resistors in parallel would dissipate more power than a 30 Ω resistor which is in series with the pair. However, combined they would dissipate less than twice the power, so that each dissipates lees than the 30 Ω resistor.