question_answer

The equivalent resistance between A and B will be:

A)  \[10\,\Omega \]              

B)  \[60\,\Omega \]

C)  \[5\,\Omega \]             

D)  \[40\,\Omega \]

Correct Answer: A

Solution :

Since given circuit is a balanced Wheatstone bridge, In the given circuit, the ratio of resistances in the opposite arms is same. \[\frac{P}{Q}=\frac{10}{10}=\frac{1}{1}\] \[\frac{R}{S}=\frac{10}{10}=\frac{1}{1}\] Thus, bridge is balanced. The given circuit now can be drawn as Here, \[10\Omega \]and \[10\Omega \] resistors are connected in series, Again, the two 200 resistors are combined in parallel, therefore equivalent resistance is given by: \[\frac{1}{R}=\frac{1}{20}+\frac{1}{20}=\frac{40}{20\times 20}=\frac{1}{10}\] \[\Rightarrow \] \[R=10\Omega \]