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. (a) `(Blv(R_(1) + R_(2)))/(R_(1)(R_(1) + R_(2))`
B. (b) `(Bl^(2)v)/(R_(1) + R_(1) R_(2))`
C. ( c) `(Blv(R_(1) + R_(2)))/(R_(1)R_(2)+ R(R_(1) + R_(2))`
D. (d) `(Bl^(2)v)/(R_(1)R_(2) + R(R_(1) + R_(2))`

Answer

C

Explanation

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