question_answer

Find the equivalent resistant between the point A and B:              

A)       \[2\,\Omega \]            

B)    \[4\,\Omega \]

C)              \[32\,\Omega \]                      

D)  \[16\,\Omega \]

Correct Answer: B

Solution :

The given circuit is reccrawn and solve as shown in the figure. Clearly it is a balanced Wheatstone bridge hence \[10\Omega \]resistance is ineffective. In the upper arm \[4\Omega \] and \[8\Omega \]. resistance are in series their effective resistance is.             \[{{R}_{u}}=4+8=12\Omega .\] Similarly, in the lower arm, resistance \[2\Omega .\] and \[4\Omega \] are also in series their effective resistance is             \[{{R}_{L}}=2+4=6\Omega \] Now, resistance \[{{R}_{u}}\] and \[{{R}_{L}}\] are in parallel. So, resultant resistance between points A and B is             \[{{R}_{AB}}=\frac{{{R}_{u}}{{R}_{L}}}{{{R}_{u}}+{{R}_{L}}}=\frac{12\times 6}{12+6}=4\Omega \]