question_answer

An infinite ladder network is arranged with resistances R and 2 R as shown.  The effective resistance between terminals A and B is                                                                [AMU (Med.) 1999]

A)         ¥                                       

B)         R

C)         2 R                                    

D)         3 R

Correct Answer: C

Solution :

                                         Let equivalent resistance between A and B is R', so given circuit can be reduced as follows                    \[R'=R+\frac{2R\times {R}'}{(2R+{R}')}\Rightarrow {{{R}'}^{2}}-R{R}'-2{{R}^{2}}=0\]                                                    On solving the equation we get \[R'=2R\].