question_answer

In the network shown in the figure, each of the resistances is equal to\[2\Omega \]. The resistances between the points A and B is

A)  \[4\,\Omega \]                        

B)  \[3\,\Omega \]

C)  \[2\,\Omega \]                        

D)  \[1\,\Omega \]

Correct Answer: C

Solution :

It is a balanced Wheatstone's bridge. The equivalent circuit is shown in the figure. The diagonal resistance, which is the galvanometer arm in Wheatstone's bridge becomes ineffective, when the bridge is balanced. \[{{R}_{PCQ}}=2+2=4\,\Omega \] \[{{R}_{PDQ}}=2+2=4\,\Omega \] APCQB and APDQB are in parallel.             \[{{R}_{AB}}=\frac{4\times 4}{4+4}=2\Omega \]