How Do You Calculate the Variable Resistance for Optimal Battery Charging?

[jesuslovesu]

Homework Statement

http://img2.freeimagehosting.net/uploads/bf073a5eb1.png
http://img2.freeimagehosting.net/uploads/bf073a5eb1.png

Determine the variable resistance R if the 25 Watts to be absorbed by the battery (0.035 ohm resistor and the 10.5 V element).

Homework Equations

V = IR
P = IV

The Attempt at a Solution

Well I did KVL clockwise current flow
-13 + 0.02*i + iR + 0.035*i + 10.5 = 0
2.5 = 0.02i + 0.035i + iR

Then factoring in 25W=10.5*i
i = 2.381 A which is close to the answer but doesn't factor in 0.035 and I'm not sure how to do it

 

[kamerling]

The Attempt at a Solution

Well I did KVL clockwise current flow
-13 + 0.02*i + iR + 0.035*i + 10.5 = 0
2.5 = 0.02i + 0.035i + iR

Then factoring in 25W=10.5*i
i = 2.381 A which is close to the answer but doesn't factor in 0.035 and I'm not sure how to do it

The question was to compute R such that you got 25 W dissipated in the 10.5V battery. You computed what the current through this battery must be. Now use that in the equation with i and R you wrote above