A) infinite
B) 2\[\Omega \]
C) \[\frac{1+\sqrt{5}}{2}\Omega \]
D) zero
Correct Answer: C
Solution :
Let\[x\]be the equivalent resistance of entire network between\[A\]and\[B\]. Hence, we have \[{{R}_{AB}}=1+\]resistance of parallel combination of\[1\Omega \]and\[x\Omega \] \[\therefore \] \[{{R}_{AB}}=1+\frac{x}{1+x}\] \[\therefore \] \[x=1+\frac{x}{1+x}\] \[\Rightarrow \] \[x+{{x}^{2}}=1+x+x\] \[\Rightarrow \] \[{{x}^{2}}-x-1=0\] \[\Rightarrow \] \[x=\frac{1+\sqrt{1+4}}{2}=\frac{1+\sqrt{5}}{2}\Omega \]You need to login to perform this action.
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