$\text{Potential difference across a conductor of length l is } \xi = Blv$

$\text{Equivalent Resistance across rod is }R_{eq} = R + \frac{R_1R_2}{R_1+R_2}$

$ I = \frac{Blv}{R + \frac{R_1R_2}{R_1+R_2}} = \frac{Blv(R_1+R_2)}{R_1R_2+R(R_1+R_2)}$