question_answer

The effective resistance between points P and Q of the electrical circuit shown in the figure is                                                               [IIT-JEE (Screening) 2002]

A)            \[2Rr/(R+r)\]

B)            \[8R\,(R+r)/(3R+r)\]

C)            \[2r+4R\]

D)            \[5R/2\,\,+\,2r\]

Correct Answer: A

Solution :

                   In a circuit, any circuit element placed between points at the same potential can be removed, without affecting the rest of the circuit. Here, by symmetry, points A, B and C are at same potential, for any potential difference between P and Q. The circuit can therefore be reduced as shown below Effective resistance \[{{R}_{eq}}=\frac{2Rr}{R+r}\].