question_answer

Find the equivalent resistance between the points A and B:

A)  \[2\,\Omega \]                               

B)         \[4\,\Omega \]               

C)         \[8\,\Omega \]                               

D)         \[16\,\Omega \]

Correct Answer: B

Solution :

The given circuit is redrawn as shown in the fig. It is balanced Wheatstone bridge, therefore \[10\Omega \] resistance is ineffective. In the upper arm \[4\Omega \] and \[8\Omega \] are in series, their effective resistance is                 \[{{R}_{U}}=4+8=12\Omega \] Similarly, in the lower arm resistances \[2\Omega \]and\[4\Omega \] are also in series their effective resistance is                 \[{{R}_{L}}=2+4=6\Omega \] Now, resistances R,- and K, are in parallel. So resultant resistance between points\[A\]and\[B\]is                 \[{{R}_{AB}}=\frac{{{R}_{U}}{{R}_{L}}}{{{R}_{U}}+{{R}_{L}}}\]                      \[=\frac{12\times 6}{12+6}=4\Omega \]