# Power and Resistance

1. Mar 8, 2016

### mattbeatlefreak

1. The problem statement, all variables and given/known data
Rank the resistors according to to the rate at which energy is dissipated in them.

2. Relevant equations
P = I2R
P = V2/R
Iin=Iout at a node

3. 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!

2. Mar 8, 2016

### 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

3. Mar 8, 2016

### mattbeatlefreak

The equivalant 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]?

4. Mar 8, 2016

exactly

5. Mar 8, 2016

### SammyS

Staff Emeritus
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.

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