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Resistances of $$2\,\Omega$$ and $$3\,\Omega$$ are connected in series between terminals A and B, and a potential difference of $$20\text{ V}$$ is applied between the terminals. An unknown resistance is connected in parallel to the $$3\,\Omega$$ resistance and the current in this unknown resistance is $$\frac{5}{12}$$ times the current that was flowing from A to B before it was connected. Find the unknown resistance (in ohm).
Correct Answer: 6
Initially the current is $$\frac{20}{5} = 4\text{ A}$$, so the current in the unknown resistance $$X$$ must be $$\frac{5}{12} \times 4 = \frac{5}{3}\text{ A}$$. With $$X$$ across the $$3\,\Omega$$, the total current is $$\frac{20}{2 + \frac{3X}{3 + X}}$$ and the share through $$X$$ is $$\frac{3}{3 + X}$$ of it, i.e. $$\frac{60}{6 + 5X}$$. Setting $$\frac{60}{6 + 5X} = \frac{5}{3}$$ gives $$X = 6\,\Omega$$.
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