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. (a) `(1)/(4)`
B. (b) `(1)/(2)`
C. ( c) `(1)/(3)`
D. (d) `0`

Answer

C

Explanation

(c ) emf induced between centre of the ring and the rim is
`e = (1)/(2)BomegaR^(2) = (1)/(2)(50)(20)(0.1)^(2) = 5V`

Now the cicuit can be drawn as follows:

``:.` I = (5) + (10 + 5) = (1)/(3)A`