A rectangular loop with a sliding conductor of length `l` is located in a uniform magnetic field perpendicular to the plane of the loop . The magneitc inducetion is `b`. The resistances `R_(1)` and `R_(2)`, respectively. Find the current through the conductor during its motion to the right with a constant velocity `v`.

Options

A. `(Blv(R_(1)+R_(2)))/(R_(1)(R_(1)+R_(2)))`
B. `(Bl^(2)v)/(R_(1)+R_(1)R_(2))`
C. `(Blv(R_(1)+R_(2)))/(R_(1)R_(2)+R(R_(1)+R_(2)))`
D. `(Bl^(2)v)/(R_(1)R_(2)+R(R_(1)+R_(2)))`

Answer

C

Explanation

Induced emf `= Blv.R` is internal resistance of seat of emf, i.e., of rod
Total resistance of circuit `= R+(R_
(1)R_(2))/(R_(1)+R_(2))`
`:. I = (Blv)/(R+(R_(1)R_(2))/((R_(1)+R_(2)))) = (Blv(R_(1)+R_(2)))/(R_(1)R_(2)+R(R_(1)+R_(2)))`