question_answer

Equivalent resistance between A and B of circuit shown in figure.

A)  \[25\,\Omega \]                             

B)  \[35\,\Omega \]

C)  \[10\,\Omega \]                             

D)  \[5\,\Omega \]

Correct Answer: D

Solution :

\[{{R}_{1}}=5\Omega \] and \[{{R}_{2}}=5\Omega \] resistances are in series,                 \[\therefore \]  \[R'=5+5=10\Omega \]                 \[R'\] and \[{{R}_{3}}=10\Omega \] are in parallel                 \[\frac{1}{R'\,'}=\frac{1}{10}+\frac{1}{10}=\frac{2}{10}=\frac{1}{5}\]                 \[R''=5\Omega \] Now,\[R'\,'\] and  \[{{R}_{4}}=5\Omega \]are in series \[\therefore \]  \[R'\,'\,'=5+5=10\Omega \] Now, \[{{R}_{5}}\] and \[R'\,'\,'\] are in parallel, \[\therefore \]  \[\frac{1}{R}=\frac{1}{10}+\frac{1}{10}=\frac{2}{10}=\frac{1}{5}\] \[\therefore \]  \[R=5\Omega \]