# Two unknown resistors. Need to find values of resistors.

## Homework Statement

When two unknown resistors are connected in series with a battery, the battery delivers 260 W and carries a total current of 5.00 A. For the same total current, 35.0 W is delivered when the resistors are connected in parallel. Determine the values of the two resistors.

P = I^2 x R

## The Attempt at a Solution

I tried to make two unknowns by plugging in numbers into the equations, but that's not working. I know that the voltage will be the same throughout the parallel circuit, and that the current will be the same throughout the series circuit, but I'm not quite sure where to go from there.

jgens
Gold Member
Since P = I2R, we can solve for the equivalent resistance of the resistors.

Req = P/I2

When the resistors are in series, r1 + r2 = Req

Construct a similar equation for when the resistors are in parallel and you can solve for the values of the two resistors.

I have my two equations, but I'm having trouble putting the two equations together. I have r1 + r2 = 7 and 1/r1 + 1/r2 = 1/52

jgens
Gold Member
I'm not certain those values are correct, maybe I've made a mistake?

For series I get, Req = P/I2 = (260 W)/(5 A)2 = 10.4 ohms.

For parallel I get, Req = P/I2 = (35 W)/(5 A)2 = 1.4 ohms.

To get you started on solving the two equations, we know that R1 + R2 = 10.4 and R1R2/(R1 + R2) = 1.4. Combine these two equations.

just solve for r1 and substitute into the other....

but are you sure those figures are correct? how did you get them?

I think I must have forgotten to square "I"...your figures are correct. But then don't you also have to take into consideration that when you do 1/r1 + 1/r2 , that it equals 1/Req? ?

jgens
Gold Member
Unless I've misunderstood your question which is certainly possible, I believe the equation Req = R1R2/(R1 + R2) takes care of that consideration.

Oh. Okay. I missed that. Thank you so much!

jgens
Gold Member
No problem!