question_answer

Seven resistances are connected as shown in the given figure. The equivalent resistance between A and B is

A) 3\[\Omega \]

B)                                       4\[\Omega \]                    

C)       4.5\[\Omega \]                

D)       15\[\Omega \]

Correct Answer: B

Solution :

Equivalent resistance of \[{{R}_{1}}\] and \[{{R}_{2}}\] (in parallel is given by \[R=\frac{6\times 6}{6+6}=3\Omega \] Equivalent resistance of \[{{R}_{5}}\] and \[{{R}_{7}}\] (in parallel)                 \[R=\frac{10\times 10}{10+10}=5\Omega \] Now, the circuit is reduced to Now, this circuit can be shown as it is balanced \[\left( \frac{5}{3}=\frac{5}{3} \right)\] Total resistance between AB \[{{R}_{AB}}=\frac{(5+3)(5+3)}{(5+3)+(5+3)}\] \[=\frac{8\times 8}{8+8}=4\Omega \]