What is the Ratio of Resistances in a Series Circuit with 20% Power Dissipation?

[KidCudi11]

Hey guys so I'm new here but really need help with just with a confirmation on the answer on this question.

Homework Statement

Two resistors R1 and R2 are connected in series and these are connected in series to a battery. If 20% of the power coming from the battery is dissipated through the R1 resistor, determine the ratio R1/R2.

Homework Equations

R=V/I (just moved around Ohms Law)

The Attempt at a Solution

Well since the resistor is in a series you normally would add them together. Since you lose 20% of the power through the first resistor you have 80% left. So I'm not positive but i figured you would just divide 20/80 and you end up with 0.25. Thanks for the help I appreciate it.

 

[jambaugh]

Be careful with that reasoning. Power dissipation is VI = R I^2. Set up the equation for current in terms of R1 R2 and the voltage of the battery V. Write the ratio of powers expressed in terms of the resistances and the current and the value of V should cancel as should the currents. You'll get an expression for the ratio in terms of the Resistances R1 and R2. You can then solve that equation for R1 i.t.o. R2 or vice versa and work out their ratio. It may end up being as your intuition reasoned but you will be using fact and not intuition. (Or it may be completely different. Don't assume, Do The Math!)