A) \[\frac{8}{7}\Omega \]
B) \[\frac{7}{8}\Omega \]
C) \[\frac{7}{4}\Omega \]
D) \[\frac{4}{9}\Omega \]
Correct Answer: A
Solution :
First resistance \[{{R}_{1}}=2\Omega \] Second resistance \[{{R}_{2}}=4\Omega \] Third resistance \[{{R}_{3}}=8\Omega \] (given) These three resistances are connected in parallel. As the relation for the equivalent resistance of parallel combination is given by \[\frac{1}{R}=\frac{1}{{{R}_{1}}}+\frac{1}{{{R}_{2}}}+\frac{1}{{{R}_{3}}}=\frac{1}{2}+\frac{1}{4}+\frac{1}{8}\] \[=\frac{7}{8}\] Thus \[R=\frac{8}{7}\Omega \]
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