Question

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

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

Answer 1

Answer: (A)

The combination of resistances is shown in figure.

Maximum resistance will be between $P$ and $Q.$
$R_{PQ}=\frac{R\left(\frac{R}{3}+\frac{R}{2}\right)}{R+\frac{R}{3}+\frac{R}{2}}=\frac{5R^2/6}{11R/6}=\frac{5R}{11}$
$R_{QR}=\frac{\frac{R}{2}\left(R+\frac{R}{3}\right)}{11R/6}=\frac{2R^2/3}{11R/6}=\frac{4R}{11}$
$R_{PR}=\frac{\frac{R}{3}\left(R+\frac{R}{2}\right)}{11R/6}$
$=\frac{R^2/2}{11R/6}=\frac{3R}{11}$
Hence, the maximum value lies between $P$ and $Q.$