Six identical resistors are connected as shown in the figure. The equivalent resistance will be

Options

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

Answer

A

Explanation

(a) Resistance between `P` and `Q`
`R_(PQ) = R || ((R )/(3) + (R )/(2)) = (R xx (5)/(6) R)/(R + (5)/(6) R) = (5)/(11) R`
Resistance between `Q` and `R`
`R_(PQ) = (R )/(2) || (R +(R )/(3)) = ((R )/(3) xx (4 R)/(3))/((R )/(2) + (4R)/(3)) = (4)/(11) R`
Resistance between `P` and `R`
`R_(PR) = (R )/(3) || ((R )/(2) + R) = ((R )/(3) xx (3R)/(2))/((R )/(3) + (3R)/(2)) = (3)/(11) R`
Hence it is clear that `P_(PQ)` is maximum.