question_answer

What is the equivalent resistance between A and B in the given circuit?

A)  \[4\,\Omega \]                          

B)  \[2\,\Omega \]

C)  \[\frac{8}{3}\,\Omega \]                                   

D)  \[\frac{3}{3}\,\Omega \]

Correct Answer: C

Solution :

\[{{R}_{1}}\] and \[{{R}_{2}}\] are in series \[{{R}_{12}}\,={{R}_{1}}+{{R}_{2}}=4\Omega \]      \[{{R}_{12}}\] and \[{{R}_{3}}\] are in parallel \[{{R}_{123}}\,=\frac{{{R}_{3}}\times {{R}_{12}}}{{{R}_{3}}+{{R}_{12}}}\,=\frac{4\times 4}{4+4}\,=2\Omega \] \[{{R}_{123}}\] and \[{{R}_{4}}\] are in series \[{{R}_{1234}}\] and \[{{R}_{5}}\] are in parallel \[{{R}_{12345}}\,=2\Omega \] \[{{R}_{12345}}\] and \[{{R}_{6}}\] are in series, \[2\Omega +2\Omega \,=4\Omega \,={{R}_{123456}}\] now, \[{{R}_{123456}}\] and \[{{R}_{7}}\] are in parallel             \[{{R}_{comb}}\,\frac{4\times 8}{4+8}\,=\frac{8}{3}\Omega \]