# Resistor power dissipation

#### stoopkid

Joined Mar 3, 2011
146
So say I have 12v with 300ohm resistor. That's (12^2)/300 = 480mW. I think.

So say it's 3 100ohm resistors in series. Is the power dissipation for each 480mW or is is 430/3 each?

Say it is 6 200ohm resistors, each 2 in parallel and each pair in series. What is the dissipation of each resistor there?

Thanks.

#### toffee_pie

Joined Oct 31, 2009
215
for part #1 its 48mW, part 2 Pt = 432uW

#### bertus

Joined Apr 5, 2008
20,673
Hello,

You can calculate the voltage accross each resistor.
The resistors are equal so the voltage on each resistor is 12 Volts / 3 = 4 Volts.
The power in each resistor is (4 Volts * 4 Volts) / 100 Ohms = 0.16 Watt each.
For the 200 Ohms resistors it is (4 Volts * 4 Volts) / 200 Ohms = 0.08 Watt each.

Bertus

#### toffee_pie

Joined Oct 31, 2009
215
for part 2, 100R in series, PT = 4.3W, or 1.43W each.
?

#### takao21203

Joined Apr 28, 2012
3,695
Everyone learns math in school. 13 year old kids learn to solve weird equtations.

But applying this maths knowledge does not happen all that often.

I don't want to sound arrogant, but applying maths, think what if you use 10,000 x 0.1 Ohms resistors.

What if each dissipates 0.5 Watts. Suddenly 5000 Watts are dissipated from nowhere.

So you can solve the question for yourself pretty easily.

I don't want to criticize you. It is more like I want to criticize the education system, and how they deal with maths.

#### toffee_pie

Joined Oct 31, 2009
215
dont know what im smoking but this is what you want, as bertus said.

been so long since i did this stuff.. #### WBahn

Joined Mar 31, 2012
26,077
So say I have 12v with 300ohm resistor. That's (12^2)/300 = 480mW. I think.

So say it's 3 100ohm resistors in series. Is the power dissipation for each 480mW or is is 430/3 each?

Say it is 6 200ohm resistors, each 2 in parallel and each pair in series. What is the dissipation of each resistor there?

Thanks.
While learning to work the problem mathematically is important, it is also important to learn to estimate (or, in this case, solve) problems more intuitively and to ask if the answer makes sense.

All of you variations result in an effective resistance of 300Ω, so the circuit supplying the 12V can't tell the difference between them and delivers the same amount of power, namely 480mW, overall.

The concervation of energy means that the sum of the power dissipated by all of the resistors must equal 480mW. Symmetry says that, in each configuration, there is nothing to distinquish one resistor from another and, therefore, each resistor is dissipating the same power as each of the others. So in the first case the single 300Ω resistor is dissipating 480mW, in the second case, each of the three 100Ω resistors is dissipating 160mW, and in the third case each of the six 200Ω resistors is dissipating 80mW. If you were to take sixteen 300Ω resistors and arrange them in four parallel strings of four resistors each, then each resistor would dissipate 30mW.

Now make sure that you can work the explicit math to get these results.

#### Audioguru

Joined Dec 20, 2007
11,249
for part #1 its 48mW
No.
The power is (12 squared)/300= 480mW, not 48mW.

#### stoopkid

Joined Mar 3, 2011
146
Woah this thread is getting hostile.

Thanks guys, it was more of a resistor concept question than a math question. I wasn't sure they would divide so linearly.

I think my question has been answered, thanks again.

#### WBahn

Joined Mar 31, 2012
26,077
The power divides evenly only because all of the circuits described are perfectly symmetric. Let's say that you too seven 300Ω resistors and hooked four o fthem up in a 2x2 array (two strings in parallel with each string consisting of two in parallel) and then hooked this array in series with another resistor and put this combination in parallel with a string made up of the remaining two resistors in series. The end result would still be a 300Ω effective resistance and a total power dissipation of 480mW, but now the four resistors in the 2x2 array would dissipate 30mW while the remaining three resistors would dissipate 120mW each.

#### toffee_pie

Joined Oct 31, 2009
215
No.