question_answer

In the given circuit, each resistance is\[10\text{ }\Omega \]. The equivalent resistance between A and D is

A) \[\text{4}0\text{ }\Omega \]        

B) \[30\text{ }\Omega \]            

C)  \[20\text{ }\Omega \]         

D)  \[10\text{ }\Omega \]       

Correct Answer: B

Solution :

 Here, the path of the current is as shown: Current enters \[A\] and leaves at\[D\]. No current enters in the branches \[YC\] and \[X'B\] as their one end is not connected anywhere (the circuit is not complete for the branches). The equivalent circuit after removing these branches is as shown below: When \[YC\] is removed, the node at Y vanishes, so \[XY\] and \[YY'\] come in series. Similarly, when \[BX'\] is removed, the node at \[X\] vanishes and\[XX'\] come in series with\[XY\]. Now, \[XX'Y'\] and \[XYY'\] are in parallel. Their resultant is\[10\]. This is in series to \[AX\] and \[YX\] and \[YD\] as shown below: So,          \[{{R}_{eq}}=30\Omega \]