Find the equivalent resistance between A and B. (Figure C, above)<br>Some current enters the terminal A and leaves through B. This current splits at various junctions and flows through different resistances. If the current in the $$2\,\Omega$$ resistance is $$1\text{ A}$$, find the potential difference between A to B.
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PLACEHOLDER ANSWER - the question has two answers. From the far end, $$4 + 2 = 6\,\Omega$$ in parallel with $$3\,\Omega$$ gives $$2\,\Omega$$; adding $$4\,\Omega$$ gives $$6\,\Omega$$, in parallel with $$3\,\Omega$$ gives $$2\,\Omega$$; adding the first $$4\,\Omega$$ gives $$R_{AB} = 6\,\Omega$$. With $$1\text{ A}$$ in the $$2\,\Omega$$, the last node is at $$6\text{ V}$$, so $$2\text{ A}$$ flows in the second $$3\,\Omega$$ and $$3\text{ A}$$ in the middle $$4\,\Omega$$. The first node is at $$6 + 12 = 18\text{ V}$$, so $$6\text{ A}$$ flows in the first $$3\,\Omega$$, the total current is $$9\text{ A}$$, and $$V_{AB} = 18 + 4 \times 9 = 54\text{ V}$$ (check, $$9 \times 6 = 54$$).