question_answer

An infinite ladder network is arranged with resistances\[R\]and\[2R\]as shown. The effective resistance between terminals A and B is

A)  \[\infty \]

B)  \[R\]

C)  \[2R\]

D)  \[3R\]

Correct Answer: C

Solution :

: Let the total resistance of the infinite ladder network be Z. Subtract first step from the infinite network. The total resistance of the remaining ladder still remains to be Z. \[\therefore \]Resistance between C and\[D=\frac{2R\times Z}{2R+Z}\] Total resistance between A and \[B=R+\frac{2RZ}{2R+Z}\] \[\therefore \] \[Z=R+\frac{2RZ}{2R+Z}\] Or \[(2RZ+{{Z}^{2}})\] \[=(2{{R}^{2}}+2Z)+2RZ\] or \[{{Z}^{2}}-RZ-2{{R}^{2}}=0\] or \[(Z-2R)(Z+R)=0\] or \[Z-2R=0;\]or \[Z=2R\]