A) P and Q
B) Q and R
C) P and R
D) Any two points.
Correct Answer: A
Solution :
Let resistance of each resistor be r. Resistance in arm PQ, \[{{R}_{1}}=r\] Resistance in arm QR, \[{{R}_{2}}=\frac{r\times r}{r+r}=\frac{r}{2}\] Resistance in arm PR, \[{{R}_{3}}=\frac{1}{\frac{1}{r}+\frac{1}{r}+\frac{1}{r}}=\frac{r}{3}\] Let net resistance between P and Q is \[{{R}_{PQ}}.\] \[\frac{1}{{{R}_{PQ}}}=\frac{1}{r}+\frac{1}{\frac{r}{3}+\frac{r}{2}}=\frac{1}{r}+\frac{6}{5r}=\frac{11}{5r}\] \[\therefore \] \[{{R}_{PQ}}=\frac{5r}{11}\] Net resistance between Q and R \[{{R}_{QR}},\] \[\frac{1}{{{R}_{QR}}}=\frac{1}{\frac{r}{2}}+\frac{1}{r+\frac{r}{3}}=\frac{2}{r}+\frac{3}{4r}=\frac{11}{4r}\] \[\therefore \] \[{{R}_{QR}}=\frac{4r}{11}\] Net resistance between P and R, \[{{R}_{PR}}\] \[\frac{1}{{{R}_{PQ}}}=\frac{1}{r/3}+\frac{1}{r+r/2}=\frac{3}{r}+\frac{2}{3r}=\frac{11}{3r}\] \[\therefore \] \[{{R}_{PR}}=\frac{3r}{11}\] Hence \[{{R}_{PQ}}>{{R}_{QR}}>{{R}_{PR}}\]You need to login to perform this action.
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