question_answer

Find the equivalent resistance between the points A and B.                                                     [BHU M-2003]

A)  \[2\,\Omega \]                               

B)  \[4\,\Omega \]

C)  \[8\,\Omega \]                               

D)  \[16\,\Omega \]

Correct Answer: B

Solution :

                 Key Idea: It is a balanced Wheatstone bridge. The given circuit can be redrawn as:   The ratios of resistances in the arms are                                                 \[\frac{P}{Q}=\frac{4}{8}=\frac{1}{2}\] And                        \[\frac{2}{4}=\frac{1}{2}=\frac{R}{S}\] Hence,                  \[\frac{P}{Q}=\frac{R}{S}=\frac{1}{2}\] Therefore, bridge is balanced, so potential across\[C\]and \[D\] is same. Also \[4\,\Omega \] and \[8\,\Omega \] are connected in series and       \[2\,\Omega \] and \[4\,\Omega \] are also in series. Hence, circuit reduces to as shown. The effective resistance is  \[\frac{1}{R'}=\frac{1}{12}+\frac{1}{6}=\frac{1+2}{12}=\frac{3}{12}\] \[\Rightarrow \]\[R'=4\Omega \]