question_answer

Three resistances of 4\[\Omega \] each are connected as shown in figure. If the point D divides the resistance into two equal halves, the resistance between point A and D will be

A)  \[12\Omega \]

B)  \[6\Omega \]

C)  \[3\Omega \]

D)  \[\frac{1}{3}\Omega \]  

Correct Answer: C

Solution :

The equivalent circuit is given by \[4\Omega \] and \[2\Omega \] resistances are in series on both sides \[\therefore \]    \[4\Omega +2\Omega =6\Omega \] Then \[6\Omega \] and \[6\Omega \]resistances are in parallel on both sides \[\frac{1}{R}=\frac{1}{6}+\frac{1}{6}=\frac{2}{6}\] \[=\frac{1}{3}\] \[R=3\Omega \]