Six equal resistances are connected between points P, Q and R as shown in the figure. Then the net resistance will be maximum between

Q: Six equal resistances are connected between points $P$, $Q$ and $R$ as shown in the figure. Then the net resistance will be maximum between

a (a) 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.

SECTION - A [PHYSICS MCQ]

GSEB - English Medium

Six equal resistances are connected between points $P$, $Q$ and $R$ as shown in the figure. Then the net resistance will be maximum between

A$P$ and $Q$
B$Q$ and $R$
C$P$ and $R$
D
Any two points

IIT 2004, Diffcult

STD 11 Science
JEE
STD 12 - 3. current electricity
Physics

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