Emf V & Potential Difference in a Resistor

[CIERAcyanide]

Homework Statement

Thermal energy is to be generated in a 0.31 resistor at the rate of 11 W by connecting the resistor to a battery whose emf is 2.1 V.

(a) What potential difference must exist across the resistor?

(b) What must be the internal resistance of the battery?

Homework Equations

P = IV
V = IR

The Attempt at a Solution

I tried manipulating the variables and substituting in the equations. P =IV, 11 = IV, V= IR, 11=I^2*R, 11=I^2*.31, so i divided 11/.31 then took the square root, which was about 6 for the current. I went back and multipled V=IR, to find V=6*.31 , which was 1.86 V. I thought that to find the total potential difference i had to add the emf V given and the V i found from current and resistance, which was 1.86V + the 2.1 V emf... 3.96. But this answer is incorrect.

As for part B, I'm completely lost.

 

[Delphi51]

I share your confusion with this question! Only after reading part (b) do we learn that there is a second resistor involved - the internal resistance of the 2.1 Volt battery. So we don't have 2.1 Volts across the 0.31 ohm resistor. So it makes sense to ask what voltage we do have across it, as part (a) does. What do we know about this component? Resistance .31 Ohms, Power 11 Watts. We need a formula that relates V, R and P. One way to derive it is to start with P = IV and replace I with V/R, eliminating the I that we neither know or care to find.

 

[CIERAcyanide]

Thank you so much, I was definitely over-complicating it in my thinking. Your explanation was really clear. :)