A) P and Q
B) Q and R
C) P and R
D) Any two points
Correct Answer: A
Solution :
Resistance between P and Q \[{{R}_{PQ}}=R||\left( \frac{R}{3}+\frac{R}{2} \right)\]\[=\frac{R\times \frac{5}{6}R}{R+\frac{5}{6}R}\]\[=\frac{5}{11}R\] Resistance between Q and R \[{{R}_{QR}}=\frac{R}{2}||\left( R+\frac{R}{3} \right)\]\[=\frac{\frac{R}{2}\times \frac{4R}{3}}{\frac{R}{2}+\frac{4R}{3}}\]\[=\frac{4}{11}R\] Resistance between P and R \[{{R}_{PR}}=\frac{R}{3}||\left( \frac{R}{2}+R \right)\]\[=\frac{\frac{R}{3}\times \frac{3R}{2}}{\frac{R}{3}+\frac{3R}{2}}\]\[=\frac{3}{11}R\] Hence it is clear that \[{{P}_{PQ}}\] is maximum.
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