question_answer

If you are provided three resistances \[2\,\Omega ,\,3\,\Omega \]and \[6\,\Omega .\]. How will you connect them, so as to obtain the equivalent resistance of \[4\,\Omega .\]?

A)  

B)   

C)  

D)  None of these

Correct Answer: C

Solution :

 In the given question in option (c), \[3\,\Omega \]. and \[6\,\Omega \]resistances are in parallel, hence equivalent resistance is \[\frac{1}{R}=\frac{1}{6}+\frac{1}{3}=\frac{9}{18}\] \[\Rightarrow \] \[R=2\,\Omega \] The two \[2\,\Omega \]. resistances are now connected in series, hence equivalent resistance is \[R=2\,\Omega +2\,\Omega =4\,\Omega \] Note: The value of the equivalent resistance of the resistances connected in parallel is less than the value of the smallest resistance among those resistances.