A metal rod of resistance `20 Omega` is fixed along a diameter of a conducting ring of radius `0.1 m` and lies on `x-y` plane. There is a magnetic field `vec(B) = (50 T)vec(k)`. The ring rotates with an angular velocity `omega = 20rad s^(-1)` about its axis. An external resistance of `10 Omega` is connected across the center of the ring and rim. The current external resistance is

Options

A. `(1)/(4)`
B. `(1)/(2)`
C. `(1)/(3)`
D. zero

Answer

C

Explanation

Potential defference berween centre of the ring and the rim is
`V=(1)/(2)BomegaR^(2)`
`=(1)/(2)(50)(2)(0.1)^(2)=5V`
now the circuit can be drawn as follows:
:. `i=(5)/(10=5)=(1)/(3)A`