First slide

combination of resistance

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

Moderate

A

P and Q
B

Q and R
C

P and R
D

any two points

Solution

Resistance between P and Q
$R_{PQ} = R | | (\frac{R}{3} + \frac{R}{2}) = \frac{R \times \frac{5}{6} R}{R = \frac{5}{6} R} = \frac{5}{11} R$
Resistance between Q and R,
$R_{RQ} = \frac{R}{2} | | (R + \frac{R}{3}) = \frac{\frac{R}{2} \times \frac{4 R}{3}}{\frac{R}{2} + \frac{4 R}{3}} = \frac{4}{11} R$
$Resistance between P and R,$
$R_{PR} = \frac{R}{3} | | (\frac{R}{2} + R) = \frac{\frac{R}{3} \times \frac{3 R}{2}}{\frac{R}{3} + \frac{3 R}{2}} = \frac{3}{11} R$
Hence it is clear that R_PQ is maximum.

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