A wire of 18`Omega` resistor is bent in a circle. Find effective resistance between A and B. `angle AOB = 60^(@)`

Options

A. `3 Omega`
B. `2.5 Omega`
C. `15 Omega`
D. `18 Omega`

Answer

B

Explanation

`2.5 Omega`
Resistance of minor arc AB of wire
`= (18 xx 60)/(360) = 3 Omega`
`therefore `Resistance of major are = `15 Omega`
Now equivalent resistance between A and B is
`R_(AB) = (3 xx 15)/(3 + 15) = (45)/(18) = (5)/(2) = 2.5 Omega`