Question

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 $

Answer 1

Answer: (B)

$ \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=2 R\, \Omega $
$R_{\text {net }} =R_{P}+R_{S} $
$=2 R+\frac{R}{3}=\frac{7 R}{3} \,\Omega$