| Six equal resistances are connected between points P, Q and R a shown in figure. The net resistance will be maximum between: [JEE ONLINE 25-04-2013] |
 |
A) P and R
B) P and Q
C) Q and R
D) any two points
Correct Answer: C
Solution :
| [b] Resistance between P and Q |
| \[{{r}_{PQ}}={{r}_{11}}\left( \frac{r}{3}+\frac{r}{2} \right)=\frac{r\times \frac{5}{6}r}{r+\frac{5}{6}r}=\frac{5}{11}r\] |
| Resistance between Q and R |
| \[{{r}_{QR}}=\frac{r}{2}11(r+\frac{r}{3})=\frac{\frac{r}{2}\times \frac{4}{3}r}{\frac{r}{2}+\frac{4}{3}r}=\frac{4}{11}r\] |
| Resistance between P and R |
| \[{{r}_{PR}}=\frac{r}{3}11\left( \frac{r}{2}+r \right)=\frac{\frac{r}{3}\times \frac{3}{2}r}{\frac{r}{3}+\frac{3}{2}r}=\frac{3}{11}r\] |
| Hence, it is clear that \[{{r}_{PQ}}\]is maximum |
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