question_answer

In the given circuit, what will be the equivalent resistance between the points A and B?

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

B)  \[\frac{20}{3}\Omega \]

C)  \[\frac{10}{5}\Omega \]                              

D)  \[5\,\Omega \]

Correct Answer: A

Solution :

                 Key Idea: Given circuit is a balanced Wheat- stone bridge. Taking the ratio of resistance's in the opposite arms, we have                 \[\frac{P}{Q}=\frac{2}{3}\]                 \[\frac{R}{S}=\frac{4}{6}=\frac{2}{3}\] Since, \[\frac{P}{Q}=\frac{R}{S}=\frac{2}{3}\], the circuit is balanced. The given circuit now reduces is as show \[R'=2+3=5\,\Omega \] \[R''=4+6=10\,\Omega \] The resistances R' and R" are now in parallel \[\therefore \]  \[\frac{1}{R}=\frac{1}{R'}+\frac{1}{R''}\]                 \[=\frac{1}{5}+\frac{1}{10}\]                 \[=\frac{2+1}{10}=\frac{3}{10}\] \[\Rightarrow \]               \[R=\frac{10}{3}\Omega \]