Algebra mistake? The answer is11.8ohm for (a).
What is V?
If V equal to supply voltage, then the maximum current in the circuit is 0.2A.
I would suggest that you avoid introducing the resistance of the rod.
For part (a), you know the current through both the resistor and the rod is 0.40 A. You have a formula that allows you to calculate the voltage across the rod if you know the current. So, see what you get for the voltage across the rod.
Kirchhoff says the sum of the voltages across the resistor and the rod must add to what?
So, you should be able to deduce the voltage across the resistor. If you know the voltage and the current for the resistor, how can you get the resistance of the resistor?
At the bottom of the first page of your notes, the denominator should be 15 - R rather than R - 15.
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