`AB` is a resistanceless conducting rod which forms a diameter of a conducting ring of radius `r` rotating in a uniform magnetic field `B` as shown in figure. The resistance `R_(1)` and `R_(2)` do not rotate. Then the current through the resistor `R_(1)` is

Options

A. (a) `(Bomegar^(2))/(2R_(1)
B. (b) `(Bomegar^(2))/(2R_(2)`
C. (c ) `(Bomegar^(2))/(2R_(1)R_(2))(R_(1) + R_(2))`
D. (d) `(Bomegar^(2))/(2(R_(1)+ R_(2))`

Answer

D

Explanation

(a) The equivalent diagram is

The induced emf across th ecenter and any point on the circumference is
`|vec(e)| = (1)/(2)Bomegal^(2) = (Bomegar^(2))/(2)`
`:.` Current through `R_(1) = (Bomegar^(2))/(2R_(1))`