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