question_answer

Five resistances of resistance\[R\,\Omega \] are there, 3 are connected in parallel and are joined to them in series. Find resultant resistance:

A)  \[\left( \frac{3}{7} \right)R\,\Omega \]                

B)         \[\left( \frac{7}{3} \right)R\,\Omega \]

C)         \[\left( \frac{7}{8} \right)R\,\Omega \]                

D)         \[\left( \frac{8}{7} \right)R\,\Omega \]

Correct Answer: B

Solution :

\[\frac{1}{{{R}_{P}}}=\frac{1}{R}+\frac{1}{R}+\frac{1}{R}=\frac{3}{R}\] \[\Rightarrow \]               \[{{R}_{P}}=\frac{R}{3}\Omega \]                  \[{{R}_{5}}=R+R=2R\Omega \]                 \[{{R}_{net}}={{R}_{P}}+{{R}_{S}}\]                        \[=2R+\frac{R}{3}=\frac{7R}{3}\Omega \]