A) \[\frac{AB}{B-A}\]
B) \[\frac{AB}{A-B}\]
C) \[\frac{A+B}{AB}\]
D) None of these
Correct Answer: A
Solution :
When n resistors are connected in parallel, then \[\frac{1}{{{R}_{1}}}+\frac{1}{{{R}_{2}}}+....\,\,\,+\,\frac{1}{{{R}_{n-1}}}+\frac{1}{{{R}_{n}}}=\frac{1}{A}\] ... when nth resistor is removed, then \[\frac{1}{{{R}_{1}}}+\frac{1}{{{R}_{2}}}+....\,\,\,+\,\frac{1}{{{R}_{n-1}}}=\frac{1}{B}\] ? Subtracting from , we get \[\frac{1}{{{R}_{n}}}=\frac{1}{A}-\frac{1}{B}\,\,\Rightarrow \,\,\,{{R}_{n}}=\frac{AB}{B-A}\]
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