A) Network (i)
B) Network (ii)
C) Network (iii)
D) All have equal equivalent resistance.
Correct Answer: C
Solution :
\[{{R}_{1}}=1\,k\Omega +200\Omega \] \[=1000\,\Omega +200\Omega =1200\Omega \] \[\frac{1}{{{R}_{i}}}=\frac{1}{1200}+\frac{1}{1000}=\frac{11}{6000}\] \[\therefore \]\[{{R}_{i}}=\frac{6000}{11}=545.45\Omega \] (ii) \[\frac{1}{{{R}_{ii}}}=\frac{1}{1000}+\frac{1}{200}+\frac{1}{1000}=\frac{7}{1000}\] \[\therefore \]\[{{R}_{ii}}=\frac{1000}{7}=142.85\Omega \] (iii) \[\frac{1}{{{R}_{1}}}=\frac{1}{1000}+\frac{1}{1000}=\frac{2}{1000}\] \[{{R}_{1}}=\frac{1000}{2}=500\Omega \] \[{{R}_{iii}}=500+200=700\Omega \] \[\therefore \]\[{{R}_{iii}}>{{R}_{i}}>{{R}_{ii}}\]
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