Question

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

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

Answer 1

The correct option is A $P$ and $Q$

Resistance between $P$ and $Q$

$R_{PQ}=R||(\frac{R}{3}+\frac{R}{2})=\frac{R\times \frac{5}{6}R}{R+\frac{5}{6}R}=\frac{5}{11}R$

Resistance between $Q$ and $R$

$R_{QR}=\frac{R}{2}||(R+\frac{R}{3})=\frac{\frac{R}{2}\times \frac{4R}{3}}{\frac{R}{2}+\frac{4R}{3}}=\frac{4}{11}R$

Resistance between $P$ and $R$

$R_{PR}=\frac{R}{3}||(\frac{R}{3}+R)=\frac{\frac{R}{3}\times \frac{3R}{2}}{\frac{R}{3}+\frac{3R}{2}}=\frac{3}{11}R$

Hence it is clear that $R_{PQ}$ is maximum.