Question

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

Answer 1

The correct option is A P and Q

In the given figure
Resistance between P and R is $\frac{R}{3}$
Resistance between R and Q is $\frac{R}{2}$
Resistance between P and Q is R

Now equivalent resistance
$R_{PQ}$ = $R\parallel (\frac{R}{3}+\frac{R}{2})$
$R_{PR}=\frac{R}{3}\parallel \left(R+\frac{R}{2}\right)$
$R_{QR}=\frac{R}{2}\parallel \left(R+\frac{R}{3}\right)$

$R_{PQ}=\frac{(\frac{R}{3}+\frac{R}{2})R}{\frac{R}{3}+\frac{R}{2}+R}=\frac{5}{11}R{R}_{PR}=\frac{(R+\frac{R}{2})\times \frac{R}{3}}{R+\frac{R}{2}+\frac{R}{3}}=\frac{3}{11}R{R}_{QR}=\frac{(R+\frac{R}{3})\times \frac{R}{2}}{R+\frac{R}{2}+\frac{R}{3}}=\frac{4}{11}R$
Then the net resistance will be maximum between P and Q.