question_answer

Five resistors are connected as shown in the given figure. The effective resistance between \[A\] and \[B\]is:

A)  \[7\,\Omega \]                               

B)  \[\frac{54}{15}\Omega \]

C)  \[\frac{10}{3}\Omega \]                                              

D)  \[17\,\Omega \]

Correct Answer: C

Solution :

Key Idea: The given Wheatstone bridge is a balanced one. In the given circuit, the ratio of resistances in the arms of the bridge is \[\frac{P}{Q}=\frac{2}{3}\]                                                    ?(1) \[\frac{R}{S}=\frac{4}{6}=\frac{2}{3}\]                                    ?(2) Since, \[\frac{P}{Q}=\frac{R}{S}=\frac{2}{3},\]hence the bridge is a balanced one. Hence,\[7\,\Omega \] resistance is avoided. The given circuit can be as follows: The \[2\,\Omega \] and \[3\,\Omega \] resistance are connected in Series, hence circuit reduces to. The \[5\,\Omega \] and \[10\,\Omega \] Resistances are in parallel                                 \[\frac{1}{R}=\frac{1}{5}+\frac{1}{10}=\frac{3}{10}\] \[\Rightarrow \]               \[R'=\frac{10}{3}\Omega \]