First slide

combination of resistance

Question

When a wire of uniform cross-section a length / and resistance R is bent into a complete circle, the resistance between any two of diametrically opposite points will be

Easy

A

R/8
B

R/4
C

R/2
D

R

Solution

It is obvious from fig. that two wires of resistances R / 2 and R / 2 are connected in parallel between two points A and 8. Therefore, the equivalent resistance between two diametrically opposite points will be
$R_{eq} = \frac{R_{1} R_{2}}{R_{1} + R_{2}} = \frac{(R / 2) \times (R / 2)}{(R / 2) + (R / 2)} or R_{eq} = \frac{R}{4}$

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