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 \[Z=2R\]You need to login to perform this action.
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