Power Dissipation in Resistors: P31.52

[Phoenixtears]

Homework Statement

Consider the circuit in Figure P31.52, in which R = 10 . The 10 resistor is dissipating 48 W of power. How much power are the other two resistors dissipating?
(Image Attached)

5 resistor ________

20 resistor ___24___

Homework Equations

VI=RP

The Attempt at a Solution

I began with the equation VI=RP. Then (I'm not even sure if I can do this!) I assumed the voltage to be constant throughout the resistors (which sounds extremely inaccurate). I was able to solve the equation for power: P= I/R. Then I used the given numbers (10 and 48W) and solved for the current: 480 amps. Placing the 'I' back into the equation I solved using the 20=R. I got the second part right with '24', but am confused why this process doesn't work for a resistor of 5.

Thank you so much in advance!

~Phoenix

 

[JaWiB]

Your equation is wrong. P=IV

 

[Phoenixtears]

Your equation is wrong. P=IV

There are multiple equations I was given in class, two are: P=IV and V=IR. But how does P=IV help me if it doesn't include resistance. I can't seem to figure out a way to include the two equations for it to work for the first part of the problem. I do realize that I can substitute I out to make P=V^2/R, but I don't see how that helps me either.

Sorry if this is obvious, I'm just so confused! I've been looking at the problem for too long probably.

Thanks again!

 

[berkeman]

You are given the power of that resistor, which gives you the voltage across it. That gives you the current through the bottom two resistors, which gives you the current through the top resistor and it's voltage and current.

Post your work and solution based on that set of hints...

 

[Phoenixtears]

Thanks for the hints.

This is where I'm at now:

I used P=V^2/R to get the voltage of the bottom resistor: 21.91.

Then, using that number and the equation P=IV I found the current: 2.19

That current is constant throughout the system. I then used the equation V=IR to find the voltage of the top: 10.95.

Then I went back to the first equation I used, P=V^2/R, to find the power of the top resistor: 23.98.

However, that's not the answer. Am I applying a concept incorrectly?

Thanks again for all the help, this is all really helpful for me.

~Phoenix

 

[berkeman]

Thanks for the hints.

This is where I'm at now:

I used P=V^2/R to get the voltage of the bottom resistor: 21.91.

Then, using that number and the equation P=IV I found the current: 2.19

That current is constant throughout the system. I then used the equation V=IR to find the voltage of the top: 10.95.

Then I went back to the first equation I used, P=V^2/R, to find the power of the top resistor: 23.98.

However, that's not the answer. Am I applying a concept incorrectly?

Thanks again for all the help, this is all really helpful for me.

~Phoenix

Your voltage is correct -- the 21.9V is the voltage across the parallel combination of the 10 and 20 Ohm resistors. The current through the parallel combination of the 10 and 20 Ohm resistors is not just 21.9V/20 Ohms ... You need to use the parallel combiination resistance...