Six equal resistances are connected between points P, Q and R as shown in figure

Question

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

Smart Achievers · Accepted Answer

(2)

$Resistance between P and Q$ $r_{P Q} = r ∥ (\frac{r}{3} + \frac{r}{2}) = \frac{r \times \frac{5}{6} r}{r + \frac{5}{6} r} = \frac{5}{11} r$

$Resistance between Q and R$ $r_{Q R} = \frac{r}{2} ∥ (r + \frac{r}{3}) = \frac{\frac{r}{2} \times \frac{4}{3} r}{\frac{r}{2} + \frac{4}{3} r} = \frac{4}{11} r$

$Resistance between P and R$ $r_{P R} = \frac{r}{3} ∥ (\frac{r}{2} + r) = \frac{\frac{r}{3} \times \frac{3}{2} r}{\frac{r}{3} + \frac{3}{2} r} = \frac{3}{11} r$

$Hence, it is clear that r_{P Q} is maximum.$

Solution

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

1 P and R

2 P and Q

3 Q and R

4 any two points

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